This thesis explores the asymptotic behavior of Conformal Field Theory (CFT) data at high energies using thermal effective action methods. Well-established results from two dimensions like Cardy formula, OPE coefficient asymptotics, and spin-refined partition function are extended to higher-dimensional theories.
\r\n\r\nIn the first part (Chapter 2), we study the asymptotic density of states formula to CFTs with continuous symmetries. Building on recent work that established the formula for finite groups, we derive universal results for compact Lie groups G. Together with checking on various theories, the formula is explained with thermal effective action.
\r\n\r\nIn the second part (Chapter 3), we develop the systematic exploration of thermal effective action methods for Cardy formula for the general dimension. Additionally, by introducing the \"hot spot hypothesis,\" shrinking circles in complex geometries act as local thermal circles, and we extends the applicability of thermal effective action from simple fibrated manifolds to diverse geometries with extreme focusing structures, opening new avenues for computing CFT observables.
\r\n\r\nIn the third part (Chapter 4), we uncover a fractal-like structure in spin-refined partition functions in higher dimension using a cutting and gluing technique, decomposing the geometry into successive quotients and identifying Kaluza-Klein vortex defects. This reveals how thermal effective action methods remain robust even for discrete geometries and rational rotations.
\r\n\r\nOur methods are purely field-theoretic and apply to both holographic and non-holographic theories. The results have implications for understanding black hole microstates in AdS/CFT, the statistics of OPE coefficients, and potential extensions of bootstrap axioms beyond traditional crossing symmetry. The thermal effective action framework studied here provides a systematic approach to computing high-energy asymptotics in CFTs, opening new avenues for exploring the structure of conformal field theories in dimensions greater than two.
" }, { "name": "Derda, Maria Dominika", "degree": "PhD", "year": "2025", "title": "Soft Theorems from Spontaneous Symmetry Breaking", "advisor": "Cheung, Clifford W.", "url": "https://resolver.caltech.edu/CaltechTHESIS:06022025-171549960", "creators": [ { "name": { "family": "Derda", "given": "Maria Dominika" }, "id": "Derda-Maria-Dominika", "orcid": "009-0007-1527-0010", "display_name": "Derda, Maria Dominika" } ], "advisors": [ { "name": { "family": "Cheung", "given": "Clifford W." }, "id": "Cheung-Clifford", "orcid": "0000-0002-9983-9425", "role": "advisor", "display_name": "Cheung, Clifford W." } ], "committee": [ { "name": { "family": "Wise", "given": "Mark B." }, "id": "Wise-M-B", "orcid": "0000-0002-9125-801X", "role": "chair", "display_name": "Wise, Mark B." }, { "name": { "family": "Simmons-Duffin", "given": "David" }, "id": "Simmons-Duffin-D", "orcid": "0000-0002-2937-9515", "role": "member", "display_name": "Simmons-Duffin, David" }, { "name": { "family": "Papucci", "given": "Michele" }, "id": "Papucci-Michele", "orcid": "0000-0003-0810-0017", "role": "member", "display_name": "Papucci, Michele" }, { "name": { "family": "Cheung", "given": "Clifford W." }, "id": "Cheung-Clifford", "orcid": "0000-0002-9983-9425", "role": "member", "display_name": "Cheung, Clifford W." } ], "option_major": [ "physics" ], "doi": "10.7907/0erh-pe17", "abstract": "Spontaneous symmetry breaking occurs when the vacuum state is not preserved under (a subset of) symmetries in the theory. Instead, the symmetry is non-linearly realized by the associated massless degrees of freedom, the Nambu-Goldstone bosons. At the level of on-shell observables, the non-linearly realized symmetry is manifested as a universal structure of scattering amplitudes in the so-called soft limit, which means sending the momenta of a Nambu-Goldstone modes to zero.
\r\n \r\nIn this dissertation, we further explore the link between spontaneous symmetry breaking and infrared dynamics of massless scalars. First, we derive soft theorems for theories with spontaneously broken Poincar\u00e9 symmetries, corresponding to effective field theories for condensed matter systems such as solids, fluids, superfluids, and framids. We also implement a bootstrap in which the enhanced vanishing of amplitudes in the soft limit is taken as an input, thus sculpting out a subclass of exceptional solid, fluid, and framid theories.
\r\n \r\nNext, we consider spontaneous breaking of higher symmetries. We derive a new sub-leading double soft pion theorem in theories with a spontaneously-broken continuous 2-group global symmetry, which intertwines amplitudes with different numbers of pions and photons. We also provide a novel derivation of the leading soft photon theorem from the Ward identity of an emergent 1-form global symmetry in effective field theories where antiparticles are integrated out.
\r\n\r\nFinally, we turn to universal features in low-energy dynamics of generic effective field theories. We extend the scalar geometric soft theorem by allowing the massless scalar to couple to other scalars, fermions, and gauge bosons. The soft theorem keeps its geometric form, but where the field-space geometry now involves the full field content of the theory. As a bonus, we also present novel double soft theorems with fermions, which mimic the geometric structure of the double soft theorem for scalars.
" }, { "name": "Shah, Nabha Niranjan", "degree": "PhD", "year": "2024", "title": "Scattering and Gravitational Effective Field Theory", "advisor": "Cheung, Clifford W.", "url": "https://resolver.caltech.edu/CaltechTHESIS:06042024-060925080", "creators": [ { "name": { "family": "Shah", "given": "Nabha Niranjan" }, "id": "Shah-Nabha-Niranjan", "orcid": "0000-0003-0458-7163", "display_name": "Shah, Nabha Niranjan" } ], "advisors": [ { "name": { "family": "Cheung", "given": "Clifford W." }, "id": "Cheung-Clifford", "orcid": "0000-0002-9983-9425", "role": "advisor", "display_name": "Cheung, Clifford W." } ], "committee": [ { "name": { "family": "Simmons-Duffin", "given": "David" }, "id": "Simmons-Duffin-D", "orcid": "0000-0002-2937-9515", "role": "chair", "display_name": "Simmons-Duffin, David" }, { "name": { "family": "Cheung", "given": "Clifford W." }, "id": "Cheung-Clifford", "orcid": "0000-0002-9983-9425", "role": "member", "display_name": "Cheung, Clifford W." }, { "name": { "family": "Wise", "given": "Mark B." }, "id": "Wise-M-B", "orcid": "0000-0002-9125-801X", "role": "member", "display_name": "Wise, Mark B." }, { "name": { "family": "Bern", "given": "Zvi" }, "id": "Bern-Zvi", "orcid": "0000-0001-9075-9501", "role": "member", "display_name": "Bern, Zvi" } ], "option_major": [ "physics" ], "doi": "10.7907/z5r7-rr17", "abstract": "Advances in the methodologies developed in quantum field theory and in the scattering amplitudes program have led to their application to questions pertaining to the classical physics of gravitationally interacting binary systems. The perturbative and relativistic nature of the quantum field theoretic setup is perfectly suited for obtaining results in an expansion in the gravitational constant, also known as the post-Minkowskian (PM) expansion. However, there are several practical scenarios where the gravitational waves produced by the inspiral or interaction of two massive bodies arise from dynamics in the strong field regime and the PM expansion breaks down. Extreme mass ratio inspirals, where a lighter body interacts with a much heavier black hole, are examples of such systems.
\r\n\r\nIn contrast, classical solutions, such as the Schwarzschild metric, and the geodesic trajectories of test bodies traversing in these nontrivial backgrounds encode information to all orders in the gravitational constant. In fact, these solutions can be viewed as the summation of certain infinite sets of Feynman diagrams from the perspective of point particle effective field theory (EFT). Alternatively, metrics and related geodesic trajectories can be seen as performing enormous simplifications of the tensor structures arising in these equivalent sets of Feynman integrals. We describe how the all order in PM information present in classical solutions can be utilized to simplify PM calculations in point particle EFT and set up a systematic framework for studying the classical dynamics of binary systems as an expansion in their mass ratio.
\r\n\r\nWe also delve into questions about the origin and scope of validity of color-kinematics duality and the double copy relation, which can be used to generate amplitudes of one theory from another. For example, graviton amplitudes can be obtained from gluon amplitudes. Unveiling the underlying structure that gives rise to these relations would not only deepen our understanding of the properties of these theories but could also serve in streamlining their application to computations of practical interest such as those showing up in the study of the gravitational two-body problem using field theory techniques. Specifically, we analyze a toy system in two dimensions where we find a Lagrangian-level manifestation of the duality in a classical equivalent of the nonlinear sigma model. We unpack the implications of an off-shell formulation of the color-kinematics duality and double copy in order to understand the possible wider implications for these relations in other theories.
" }, { "name": "Singh, Ashmeet", "degree": "PhD", "year": "2020", "title": "Quantum Mechanical Vistas on the Road to Quantum Gravity", "advisor": "Carroll, Sean M.", "url": "https://resolver.caltech.edu/CaltechTHESIS:05292020-005036817", "creators": [ { "name": { "family": "Singh", "given": "Ashmeet" }, "id": "Singh-Ashmeet", "orcid": "0000-0002-4404-1416", "display_name": "Singh, Ashmeet" } ], "advisors": [ { "name": { "family": "Carroll", "given": "Sean M." }, "id": "Carroll-S-M", "orcid": "0000-0002-4226-5758", "role": "advisor", "display_name": "Carroll, Sean M." } ], "committee": [ { "name": { "family": "Preskill", "given": "John P." }, "id": "Preskill-J", "orcid": "0000-0002-2421-4762", "role": "chair", "display_name": "Preskill, John P." }, { "name": { "family": "Hsieh", "given": "David" }, "id": "Hsieh-David", "orcid": "0000-0002-0812-955X", "role": "member", "display_name": "Hsieh, David" }, { "name": { "family": "Brandao", "given": "Fernando" }, "id": "Brand\u00e3o-F-G-S-L", "orcid": "0000-0003-3866-9378", "role": "member", "display_name": "Brandao, Fernando" }, { "name": { "family": "Carroll", "given": "Sean M." }, "id": "Carroll-S-M", "orcid": "0000-0002-4226-5758", "role": "member", "display_name": "Carroll, Sean M." } ], "option_major": [ "physics" ], "doi": "10.7907/m1vx-d174", "abstract": "In this thesis, we lay out the goal, and a broad outline, for a program that takes quantum mechanics in its minimal form to be the fundamental ontology of the universe. Everything else, including features like space-time, matter and gravity associated with classical reality, are emergent from these minimal quantum elements. We argue that the Hilbert space of quantum gravity is locally finite-dimensional, in sharp contrast to that of conventional field theory, which could have observable consequences for gravity. We also treat time and space on an equal footing in Hilbert space in a reparametrization invariant setting and show how symmetry transformations, both global and local, can be treated as unitary basis changes.
\r\n\r\nMotivated by the finite-dimensional context, we use Generalized Pauli Operators as finite-dimensional conjugate variables and define a purely Hilbert space notion of locality based on the spread induced by conjugate operators which we call \"Operator Collimation.\" We study deviations in the spectrum of physical theories, particularly the quantum harmonic oscillator, induced by finite-dimensional effects, and show that by including a black hole-based bound in a lattice field theory, the quantum contribution to the vacuum energy can be suppressed by multiple orders of magnitude.
\r\n\r\nWe then show how one can recover subsystem structure in Hilbert space which exhibits emergent quasi-classical dynamics. We explicitly connect classical features (such as pointer states of the system being relatively robust to entanglement production under environmental monitoring and the existence of approximately classical trajectories) with features of the Hamiltonian. We develop an in-principle algorithm based on extremization of an entropic quantity that can sift through different factorizations of Hilbert space to pick out the one with manifest classical dynamics. This discussion is then extended to include direct sum decompositions and their compatibility with Hamiltonian evolution.
\r\n\r\nFollowing this, we study quantum coarse-graining and state-reduction maps in a broad context. In addition to developing a first-principle quantum coarse-graining algorithm based on principle component analysis, we construct more general state-reduction maps specified by a restricted set of observables which do not span the full algebra (as could be the case of limited access in a laboratory or in various situations in quantum gravity). We also present a general, not inherently numeric, algorithm for finding irreducible representations of matrix algebras.
\r\n\r\nThroughout the thesis, we discuss implications of our work in the broader goal of understanding quantum gravity from minimal elements in quantum mechanics.
" }, { "name": "Zhang, Yongliang", "degree": "PhD", "year": "2020", "title": "Information Scrambling in Quantum Many-Body Systems", "advisor": "Chen, Xie", "url": "https://resolver.caltech.edu/CaltechTHESIS:02262020-182938837", "creators": [ { "name": { "family": "Zhang", "given": "Yongliang" }, "id": "Zhang-Yongliang", "orcid": "0000-0002-8246-3759", "display_name": "Zhang, Yongliang" } ], "advisors": [ { "name": { "family": "Chen", "given": "Xie" }, "id": "Chen-Xie", "orcid": "0000-0003-2215-2497", "role": "advisor", "display_name": "Chen, Xie" } ], "committee": [ { "name": { "family": "Brandao", "given": "Fernando" }, "id": "Brand\u00e3o-F-G-S-L", "orcid": "0000-0003-3866-9378", "role": "chair", "display_name": "Brandao, Fernando" }, { "name": { "family": "Alicea", "given": "Jason F." }, "id": "Alicea-J", "orcid": "0000-0001-9979-3423", "role": "member", "display_name": "Alicea, Jason F." }, { "name": { "family": "Chen", "given": "Xie" }, "id": "Chen-Xie", "orcid": "0000-0003-2215-2497", "role": "member", "display_name": "Chen, Xie" }, { "name": { "family": "Endres", "given": "Manuel A." }, "id": "Endres-M", "orcid": "0000-0002-4461-224X", "role": "member", "display_name": "Endres, Manuel A." } ], "option_major": [ "physics" ], "doi": "10.7907/GDZ1-0G66", "abstract": "A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems?
\r\n\r\nWe first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone.
\r\n\r\nNext, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation.
\r\n\r\nWe also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed.
\r\n\r\nFinally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.
" }, { "name": "Du, Song Ming", "degree": "PhD", "year": "2019", "title": "Fundamental Physics Through Gravitational Waves: From No-Hair Theorem to Quantum Structures of Black Holes", "advisor": "Chen, Yanbei", "url": "https://resolver.caltech.edu/CaltechTHESIS:12132018-230901638", "creators": [ { "name": { "family": "Du", "given": "Song Ming" }, "id": "Du-Song-Ming", "orcid": "0000-0003-0083-7014", "display_name": "Du, Song Ming" } ], "advisors": [ { "name": { "family": "Chen", "given": "Yanbei" }, "id": "Chen-Yanbei", "orcid": "0000-0002-9730-9463", "role": "advisor", "display_name": "Chen, Yanbei" } ], "committee": [ { "name": { "family": "Weinstein", "given": "Alan Jay" }, "id": "Weinstein-Alan-J-Physics", "orcid": "0000-0002-0928-6784", "role": "chair", "display_name": "Weinstein, Alan Jay" }, { "name": { "family": "Teukolsky", "given": "Saul A." }, "id": "Teukolsky-S-A", "orcid": "0000-0001-9765-4526", "role": "member", "display_name": "Teukolsky, Saul A." }, { "name": { "family": "Porter", "given": "Frank C." }, "id": "Porter-F-C", "orcid": "0000-0003-1948-8889", "role": "member", "display_name": "Porter, Frank C." }, { "name": { "family": "Chen", "given": "Yanbei" }, "id": "Chen-Yanbei", "orcid": "0000-0002-9730-9463", "role": "member", "display_name": "Chen, Yanbei" } ], "option_major": [ "physics" ], "doi": "10.7907/YSDX-J506", "abstract": "In general relativity, black hole is the simplest macroscopic object in the universe: any black hole can be completely described by its mass, charge and angular mo- mentum. However, such a simple picture might be changed if the gravitational field equations are modified or quantum effects are taken into consideration. These additional hairs of black hole, if exist, may provide valuable information to reveal the deepest mystery of the universe: quantum theory of gravity.
\r\n\r\nIn this thesis, we try to relate the hypothetical extra hairs of black hole with the ob- servational evidence as gravitational waves \u2013 another prediction of general relativity and are recently detected. In Chapter I, we provide a pedagogical introduction to the black hole hairs introduced by modified gravity and quantum mechanics, and lay out a mathematical framework to describe the gravitational wave emission with the existence of near-horizon quantum hair. In Chapter II we show that in scalar-tensor theory of gravity, the formation process of a black hole from gravitational collapse is accompanied with the emission of scalar hair. This mechanism gives rise to a scalar type memory effect of gravitational wave, which does not exist in general relativity. This phenomenon can further be used to study the parameter space of the scalar-tensor theory. In Chapter III, we find the scalar gravitational memory effect from stellar collapses provide the strongest sources for the stochastic gravita- tional wave background with scalar polarization in Brans-Dicke theory. The energy density spectrum for this background is provided and its model dependencies are studied. In Chapter IV, we provide a Green\u2019s function method to study the echoes, which are the gravitational waves reflected by the quantum hair near the event hori- zon of a black hole. In Chapter V, we build phenomenological models to describe the near-horizon quantum hair and predict its implication to the binary black hole stochastic gravitational wave background. Our study indicates that the existence of the quantum hair will significantly increases such a background and pins down the most relevant model parameter to be the area under the effective potential. Further, we also demonstrate that the result is rather robust against the uncertainties about the nature of the near-horizon quantum hair. In the end, a field theory based treatment to the gravitational waves in general relativity is provided as the appendix.
" }, { "name": "Heydeman, Matthew Thomas Edwin", "degree": "PhD", "year": "2019", "title": "Supersymmetric Scattering Amplitudes and Algebraic Aspects of Holography from the Projective Line", "advisor": "Schwarz, John H.; Marcolli, Matilde", "url": "https://resolver.caltech.edu/CaltechTHESIS:06102019-125514401", "creators": [ { "name": { "family": "Heydeman", "given": "Matthew Thomas Edwin" }, "id": "Heydeman-Matthew-Thomas-Edwin", "orcid": "000-0001-7033-9075", "display_name": "Heydeman, Matthew Thomas Edwin" } ], "advisors": [ { "name": { "family": "Schwarz", "given": "John H." }, "id": "Schwarz-J-H", "orcid": "0000-0001-9861-7559", "role": "advisor", "display_name": "Schwarz, John H." }, { "name": { "family": "Marcolli", "given": "Matilde" }, "id": "Marcolli-M", "orcid": "0000-0002-2045-2907", "role": "advisor", "display_name": "Marcolli, Matilde" } ], "committee": [ { "name": { "family": "Cheung", "given": "Clifford W." }, "id": "Cheung-Clifford", "orcid": "0000-0002-9983-9425", "role": "chair", "display_name": "Cheung, Clifford W." }, { "name": { "family": "Schwarz", "given": "John H." }, "id": "Schwarz-J-H", "orcid": "0000-0001-9861-7559", "role": "member", "display_name": "Schwarz, John H." }, { "name": { "family": "Marcolli", "given": "Matilde" }, "id": "Marcolli-M", "orcid": "0000-0002-2045-2907", "role": "member", "display_name": "Marcolli, Matilde" }, { "name": { "family": "Carroll", "given": "Sean M." }, "id": "Carroll-S-M", "orcid": "0000-0002-4226-5758", "role": "member", "display_name": "Carroll, Sean M." } ], "option_major": [ "physics" ], "doi": "10.7907/HFPD-JX10", "abstract": "In this thesis, we consider two topics in string theory and quantum field theory which are related by the common appearance of one-dimensional projective geometry. In the first half of the thesis, we study six-dimensional (6D) supersymmetric quantum field theories and supergravity at the leading (tree) approximation and compute the complete S-matrix for these theories as world-sheet integrals over the punctured Riemann sphere. This exploits the analytic structure of tree amplitudes which are rational and holomorphic in the kinematics and naturally related to the geometry of points on the complex projective line. The 6D n-particle S-matrix makes many symmetries and hidden properties manifest and generalizes the well-studied formulas for four-dimensional amplitudes in the form of twistor string theory and the rational curves formalism. While the systems we study are all field theories, they are in essence low-energy effective field theory limits of string theory and M-theory backgrounds. This includes theories such as those with 6D (2,0) supersymmetry which contain U(1) self-dual tensor fields which are difficult to treat from a Lagrangian point of view. Our formulas circumvent this difficulty and allow a generalization and unification of a large class of 6D scattering amplitudes which permit a sensible classical limit, including the abelian world-volume of the M-theory Five-brane. Dimensional reduction to four dimensions is also possible, leading to new formulas for 4D physics from 6D.
\r\n\r\nIn the second half of the thesis, we discuss the projective algebraic and geometric structure of the AdS3/CFT2 correspondence. In the usual statement of this correspondence, two-dimensional conformal field theory (CFT) on the Riemann sphere or a higher-genus surface is holographically dual to features of topological gravity in three dimensions with negative curvature. Since every compact Riemann surface is a projective algebraic curve, many constructions of interest in physics (which a priori depend on the analytic structure of the spacetime) can be formulated in purely algebraic language. We generalize the AdS (anti-de Sitter space)/CFT correspondence according to this principle using projective geometry over the p-adic numbers, Qp. The result is a formulation of holography in which the bulk geometry is discrete---the Bruhat--Tits tree for PGL(2,Qp)---but the group of bulk isometries nonetheless agrees with that of boundary conformal transformations and is not broken by discretization. Parallel to the usual holographic correspondence, semi-classical dynamics of fields in the bulk compute the correlation functions of local operators on the boundary. Beyond correlators on the p-adic line, we propose a tensor network model in which the patterns of entanglement on the boundary are computed by discrete geometries in the bulk. We suggest that this forms the natural geometric setting for tensor networks that have been proposed as models of bulk reconstruction via quantum error correcting codes. The model is built from tensors based on projective geometry over finite fields, Fp, and correctly computes the Ryu-Takayanagi formula, holographic entanglement and black hole entropy, and multiple interval entanglement inequalities.
\r\n\r\nIn Chapter 2, we present tree-level n-particle on-shell scattering amplitudes of various brane theories with 16 conserved supercharges which are generalizations of Dirac--Born--Infeld theory. These include the world-volume theory of a probe D3-brane or D5-brane in 10D Minkowski spacetime as well as a probe M5-brane in 11D Minkowski spacetime, which describes self interactions of an abelian tensor supermultiplet with 6D (2,0) supersymmetry. We propose twistor-string-like formulas for tree-level scattering amplitudes of all multiplicities for each of these theories, and the amplitudes are written as integrals over the moduli space of certain rational maps localized on the (n-3)! solutions of the scattering equations. The R symmetry of the D3-brane theory is shown to be SU(4) x U(1), and the U(1) factor implies that its amplitudes are helicity conserving. Each of 6D theories (D5-brane and M5-brane) reduces to the D3-brane theory by dimensional reduction. As special cases of the general M5-brane amplitudes, we present compact formulas for examples involving only the self-dual B field with n=4,6,8.
\r\n\r\nIn Chapter 3, we extend this formalism to n-particle tree-level scattering amplitudes of six-dimensional N=(1,1) super Yang--Mills (SYM) and N=(2,2) supergravity (SUGRA). The SYM theory arises on the world volume of coincident D5-branes, and the supergravity is the result of toroidal compactification of string theory. These theories have non-abelian interactions which allow for both even and odd-point amplitudes, unlike the branes of Chapter 2. Due to the properties of spinor-helicity variables in six dimensions, the even-n and odd-n formulas are quite different and have to be treated separately. We first propose a manifestly supersymmetric expression for the even-n amplitudes of N=(1,1) SYM theory and perform various consistency checks. By considering soft-gluon limits of the even-n amplitudes, we deduce the form of the rational maps and the integrand for n odd. The odd-n formulas obtained in this way have a new redundancy that is intertwined with the usual SL(2,C) invariance on the Riemann sphere. We also propose an alternative form of the formulas, analogous to the Witten--RSV (Roiban, Spradlin, and Volovich) formulation, and explore its relationship with the symplectic (or Lagrangian) Grassmannian. Since the amplitudes are formulated in a way that manifests double-copy properties, formulas for the six-dimensional N=(2,2) SUGRA amplitudes follow. These six-dimensional results allow us to deduce new formulas for five-dimensional SYM and SUGRA amplitudes, as well as massive amplitudes of four-dimensional N=4 SYM on the Coulomb branch.
\r\n\r\nIn Chapter 4, we consider half-maximal supergravity and present a twistor-like formula for the complete tree-level S matrix of chiral 6D (2,0) supergravity coupled to 21 abelian tensor multiplets. This is the low-energy effective theory that corresponds to Type IIB superstring theory compactified on a K3 surface. As in previous chapters, the formula is expressed as an integral over the moduli space of certain rational maps of the punctured Riemann sphere; the new ingredient is an integrand which successfully incorporates both gravitons and multiple flavors of tensors. By studying soft limits of the formula, we are able to explore the local moduli space of this theory, SO(5,21)/(SO(5) x SO(21)). Finally, by dimensional reduction, we also obtain a new formula for the tree-level S-matrix of 4D N=4 Einstein--Maxwell theory.
\r\n\r\nIn Chapter 5, we introduce p-adic AdS/CFT and discuss several physical and mathematical features of the holographic correspondence between conformal field theories on P1(Qp) and lattice models on the Bruhat--Tits tree of PGL(2,Qp), an infinite tree of p+1 valence which has the p-adic projective line as its boundary. We review the p-adic numbers, the Bruhat--Tits tree, and some of their applications to physics including p-adic CFT. A key feature of these constructions is the discrete and hierarchical nature of the tree and the corresponding field theories, which serve as a toy model of holography in which there are no gravitons and no conformal descendants. Standard holographic results for massive free scalar fields in a fixed background carry over to the tree; semi-classical dynamics in the bulk compute correlation functions in the dual field theory and we obtain a precise relationship between the bulk mass and the scaling dimensions of local operators. It is also possible to interpret the vertical direction in the tree a renormalization-group scale for modes in the boundary CFT. Higher-genus bulk geometries (the BTZ black hole and its generalizations) can be understood straightforwardly in our setting and their construction parallels the story in AdS_3 topological gravity.
\r\n\r\nIn Chapter 6, we consider a class of holographic quantum error-correcting codes, built from perfect tensors in network configurations dual to Bruhat--Tits trees and their quotients by Schottky groups corresponding to BTZ black holes. The resulting holographic states can be constructed in the limit of infinite network size. We obtain a p-adic version of entropy which obeys a Ryu--Takayanagi like formula for bipartite entanglement of connected or disconnected regions, in both genus-zero and genus-one p-adic backgrounds, along with a Bekenstein--Hawking-type formula for black hole entropy. We prove entropy inequalities obeyed by such tensor networks, such as subadditivity, strong subadditivity, and monogamy of mutual information (which is always saturated). In addition, we construct infinite classes of perfect tensors directly from semi-classical states in phase spaces over finite fields, generalizing the CRSS algorithm. These codes and the resulting networks provide a natural bulk geometric interpretation of non-Archimedean notions of entanglement in holographic boundary states.
" }, { "name": "Wang, Zitao", "degree": "PhD", "year": "2019", "title": "Topological Phases of Matter: Exactly Solvable Models and Classification", "advisor": "Chen, Xie", "url": "https://resolver.caltech.edu/CaltechTHESIS:04242019-205929726", "creators": [ { "name": { "family": "Wang", "given": "Zitao" }, "id": "Wang-Zitao", "orcid": "0000-0002-2326-2674", "display_name": "Wang, Zitao" } ], "advisors": [ { "name": { "family": "Chen", "given": "Xie" }, "id": "Chen-Xie", "orcid": "0000-0003-2215-2497", "role": "advisor", "display_name": "Chen, Xie" } ], "committee": [ { "name": { "family": "Kapustin", "given": "Anton N." }, "id": "Kapustin-A", "orcid": "0000-0003-3903-5158", "role": "chair", "display_name": "Kapustin, Anton N." }, { "name": { "family": "Alicea", "given": "Jason F." }, "id": "Alicea-J", "orcid": "0000-0001-9979-3423", "role": "member", "display_name": "Alicea, Jason F." }, { "name": { "family": "Endres", "given": "Manuel A." }, "id": "Endres-M", "orcid": "0000-0002-4461-224X", "role": "member", "display_name": "Endres, Manuel A." }, { "name": { "family": "Chen", "given": "Xie" }, "id": "Chen-Xie", "orcid": "0000-0003-2215-2497", "role": "member", "display_name": "Chen, Xie" } ], "option_major": [ "physics" ], "doi": "10.7907/BXJR-1M62", "abstract": "In this thesis, we study gapped topological phases of matter in systems with strong inter-particle interaction. They are challenging to analyze theoretically, because interaction not only gives rise to a plethora of phases that are otherwise absent, but also renders methods used to analyze non-interacting systems inadequate. By now, people have had a relatively systematic understanding of topological orders in two spatial dimensions. However, less is known about the higher dimensional cases. In Chapter 2, we will explore three dimensional long-range entangled topological orders in the framework of Walker-Wang models, which are a class of exactly solvable models for three-dimensional topological phases that are not known previously to be able to capture these phases. We find that they can represent a class of twisted discrete gauge theories, which were discovered using a different formalism. Meanwhile, a systematic theory of bosonic symmetry protected topological (SPT) phases in all spatial dimensions have been developed based on group cohomology. A generalization of the theory to group supercohomology has been proposed to classify and characterize fermionic SPT phases in all dimensions. However, it can only handle cases where the symmetry group of the system is a product of discrete unitary symmetries. Furthermore, the classification is known to be incomplete for certain symmetries. In Chapter 3, we will construct an exactly solvable model for the two-dimensional time-reversal-invariant topological superconductors, which could be valuable as a first attempt to a systematic understanding of strongly interacting fermionic SPT phases with anti-unitary symmetries in terms of exactly solvable models. In Chapter 4, we will propose an alternative classification of fermionic SPT phases using the spin cobordism theory, which hopefully can capture all the phases missing in the supercohomology classification. We test this proposal in the case of fermionic SPT phases with Z2 symmetry, where Z2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known fermionic SPT phases in space dimensions less than or equal to 3.
" }, { "name": "Bartolotta, Anthony Leo", "degree": "PhD", "year": "2018", "title": "The Union of Quantum Field Theory and Non-Equilibrium Thermodynamics", "advisor": "Wise, Mark B.; Carroll, Sean M.", "url": "https://resolver.caltech.edu/CaltechTHESIS:05312018-124004005", "creators": [ { "name": { "family": "Bartolotta", "given": "Anthony Leo" }, "id": "Bartolotta-Anthony-Leo", "orcid": "0000-0003-4971-9545", "display_name": "Bartolotta, Anthony Leo" } ], "advisors": [ { "name": { "family": "Wise", "given": "Mark B." }, "id": "Wise-M-B", "role": "co-advisor", "display_name": "Wise, Mark B." }, { "name": { "family": "Carroll", "given": "Sean M." }, "id": "Carroll-S-M", "role": "co-advisor", "display_name": "Carroll, Sean M." } ], "committee": [ { "name": { "family": "Wise", "given": "Mark B." }, "id": "Wise-M-B", "role": "chair", "display_name": "Wise, Mark B." }, { "name": { "family": "Carroll", "given": "Sean M." }, "id": "Carroll-S-M", "role": "member", "display_name": "Carroll, Sean M." }, { "name": { "family": "Preskill", "given": "John P." }, "id": "Preskill-J", "role": "member", "display_name": "Preskill, John P." }, { "name": { "family": "Schwab", "given": "Keith C." }, "id": "Schwab-K-C", "role": "member", "display_name": "Schwab, Keith C." } ], "option_major": [ "physics" ], "doi": "10.7907/F7VT-7X41", "abstract": "Quantum field theory is the language used to describe nature at its most fundamental scales; while thermodynamics is a framework to describe the collective behavior of macroscopic systems. Recent advances in non-equilibrium thermodynamics have enabled this framework to be applied to smaller systems operating out of thermal equilibrium. This thesis is concerned with both quantum field theory and non-equilibrium thermodynamics independently and with their intersection.
\r\n\r\nFirst, a purely phenomenological application of quantum field theory is explored in the context of the upcoming Mu2E experiment. This experiment will look for rare decays which would indicate the presence of physics beyond the Standard Model. Using the language of effective field theories, a next-to-leading order analysis of the conversion rate is performed.
\r\n\r\nThe focus then shifts to an apparent paradox in the Bayesian interpretation of statistical mechanics. For a Bayesian observer making measurements of an open system, the Shannon entropy decreases, in apparent violation of the Second Law of Thermodynamics. It is shown that rather than utilizing the entropy, which can decrease under Bayesian updates, the Second Law for a Bayesian observer can be rephrased in terms\r\nof a cross-entropy which is always non-negative.
\r\n\r\nFinally, the intersection of quantum field theory and non-equilibrium thermodynamics is examined. Using quantum work fluctuation theorems, an investigation of how these frameworks can be applied to a driven quantum field theory is performed. For a time-dependent variant of \u03bb\u03c64 , analytic expressions for the work distribution functions at one-loop order are derived. These expressions are shown to satisfy the quantum Jarzynski equality and Crooks fluctuation theorem.
" }, { "name": "Chatwin-Davies, Aidan \u00c9mile", "degree": "PhD", "year": "2018", "title": "Gravity Informed", "advisor": "Carroll, Sean M.", "url": "https://resolver.caltech.edu/CaltechTHESIS:05282018-130631568", "creators": [ { "name": { "family": "Chatwin-Davies", "given": "Aidan \u00c9mile" }, "id": "Chatwin-Davies-Aidan-\u00c9mile", "orcid": "0000-0003-1406-9271", "display_name": "Chatwin-Davies, Aidan \u00c9mile" } ], "advisors": [ { "name": { "family": "Carroll", "given": "Sean M." }, "id": "Carroll-S-M", "orcid": "0000-0002-4226-5758", "role": "advisor", "display_name": "Carroll, Sean M." } ], "committee": [ { "name": { "family": "Cheung", "given": "Clifford W." }, "id": "Cheung-Clifford", "orcid": "0000-0002-9983-9425", "role": "chair", "display_name": "Cheung, Clifford W." }, { "name": { "family": "Preskill", "given": "John P." }, "id": "Preskill-J", "orcid": "0000-0002-2421-4762", "role": "member", "display_name": "Preskill, John P." }, { "name": { "family": "Weinstein", "given": "Alan Jay" }, "id": "Weinstein-Alan-J-Physics", "orcid": "0000-0002-0928-6784", "role": "member", "display_name": "Weinstein, Alan Jay" }, { "name": { "family": "Carroll", "given": "Sean M." }, "id": "Carroll-S-M", "orcid": "0000-0002-4226-5758", "role": "member", "display_name": "Carroll, Sean M." } ], "option_major": [ "physics" ], "doi": "10.7907/ZD4W-4C63", "abstract": "Formulating a universally satisfactory theory of quantum gravity is a long-standing open problem in theoretical physics. Relatively recently, the use of techniques from quantum information has emerged as a powerful tool for analyzing phenomena that lie at the intersection of quantum theory and gravitation. This thesis describes several advances and novel proposals that were made regarding information theoretic aspects of quantum gravity in three broad areas: holography, cosmology, and the black hole information problem.
\r\n\r\nRegarding holography, we first assess the differences between typical holographic states and fully random states. Next, we show that determining Ryu-Takayanagi surfaces in AdS3/CFT2 is computationally easy from a complexity-theoretic standpoint. Finally, we identify precise consistency conditions that constrain the validity of an early tensor network model for the AdS/CFT correspondence that uses the Multiscale Entanglement Renormalization Ansatz (MERA).
\r\n\r\nRegarding cosmology, we propose an alternative interpretation of the MERA as a discretization of de Sitter spacetime. Next, we return to holographic ideas and show that an appropriately-defined Generalized Second Law implies a cosmic no-hair theorem for certain classes of cosmological spacetimes. Finally, we advance an information-theoretic proposal for calculating the signature of a quantum gravity-motivated, fully covariant, natural ultraviolet cutoff in the spectrum of inflationary perturbations.
\r\n\r\nRegarding the black hole information problem, we begin by exhibiting a simple protocol which, under highly specific circumstances, allows one to retrieve a single qubit from a black hole. Next, we propose an operational resolution of the black hole information problem in which observers who enter the black hole could never detect an inconsistency between their experiences and quantum mechanics due to the finite amount of time available before reaching the central singularity. Finally, we discuss a proposal to understand the emergence of an ensemble of definite geometries during the process of black hole evaporation as a decoherence process, as well as its implications for the black hole information problem.
" }, { "name": "Kravchuk, Petr", "degree": "PhD", "year": "2018", "title": "Spin in Conformal Field Theory", "advisor": "Ooguri, Hirosi", "url": "https://resolver.caltech.edu/CaltechTHESIS:06012018-180443792", "creators": [ { "name": { "family": "Kravchuk", "given": "Petr" }, "id": "Kravchuk-Petr", "orcid": "0000-0003-0977-3686", "display_name": "Kravchuk, Petr" } ], "advisors": [ { "name": { "family": "Ooguri", "given": "Hirosi" }, "id": "Ooguri-H", "orcid": "0000-0001-6021-3778", "role": "advisor", "display_name": "Ooguri, Hirosi" } ], "committee": [ { "name": { "family": "Ooguri", "given": "Hirosi" }, "id": "Ooguri-H", "orcid": "0000-0001-6021-3778", "role": "chair", "display_name": "Ooguri, Hirosi" }, { "name": { "family": "Simmons-Duffin", "given": "David" }, "id": "Simmons-Duffin-D", "orcid": "0000-0002-2937-9515", "role": "member", "display_name": "Simmons-Duffin, David" }, { "name": { "family": "Kapustin", "given": "Anton N." }, "id": "Kapustin-A", "orcid": "0000-0003-3903-5158", "role": "member", "display_name": "Kapustin, Anton N." }, { "name": { "family": "Alicea", "given": "Jason F." }, "id": "Alicea-J", "orcid": "0000-0001-9979-3423", "role": "member", "display_name": "Alicea, Jason F." } ], "option_major": [ "physics" ], "doi": "10.7907/54MW-WY30", "abstract": "We study various questions related to operators with spin in quantum conformal field theory in dimensions higher than two. In particular, we classify conformally-invariant tensor structures which appear in correlation functions of local operators and develop tools for computation of conformal blocks which contribute to these functions. We study the crossing equations for four-point functions using numerical and analytical techniques. Finally, we explore the question of analytic continuation of local operators in spin, which leads us to a simple proof of a generalized Lorentzian inversion formula.
" }, { "name": "McKinney, Tristan James", "degree": "PhD", "year": "2018", "title": "The Effective Field Theory of Fermi Surfaces in the Vicinity of Van Hove Singularities", "advisor": "Kapustin, Anton N.", "url": "https://resolver.caltech.edu/CaltechTHESIS:06042018-162115007", "creators": [ { "name": { "family": "McKinney", "given": "Tristan James" }, "id": "McKinney-Tristan-James", "orcid": "0000-0003-2365-1810", "display_name": "McKinney, Tristan James" } ], "advisors": [ { "name": { "family": "Kapustin", "given": "Anton N." }, "id": "Kapustin-A", "orcid": "0000-0003-3903-5158", "role": "advisor", "display_name": "Kapustin, Anton N." } ], "committee": [ { "name": { "family": "Kapustin", "given": "Anton N." }, "id": "Kapustin-A", "orcid": "0000-0003-3903-5158", "role": "chair", "display_name": "Kapustin, Anton N." }, { "name": { "family": "Wise", "given": "Mark B." }, "id": "Wise-M-B", "orcid": "0000-0002-9125-801X", "role": "member", "display_name": "Wise, Mark B." }, { "name": { "family": "Spiropulu", "given": "Maria" }, "id": "Spiropulu-M", "orcid": "0000-0001-8172-7081", "role": "member", "display_name": "Spiropulu, Maria" }, { "name": { "family": "Motrunich", "given": "Olexei I." }, "id": "Motrunich-Olexei", "orcid": "0000-0001-8031-0022", "role": "member", "display_name": "Motrunich, Olexei I." } ], "option_major": [ "physics" ], "doi": "10.7907/8VWF-V806", "abstract": "The use of effective field theories to attack new and seemingly disparate problems has proliferated in the past several decades. In this thesis, we develop effective field theories for systems of fermionic quasiparticles possessing Fermi surfaces, with a particular focus on Fermi surfaces proximal to Van Hove singularities. Such systems are a fruitful source of complex and novel behavior in condensed matter physics. We begin with an overview of the renormalization group procedure at the heart of effective field theory by analyzing a simple example. We emphasize the concept that the RG relates the observables of one theory to those of another theory with precisely the same form but different numerical parameters. We also note the generality and extensibility of these concepts. We then apply this perspective to the study of quasiparticles with a round Fermi surface, employing the technique of binning the quasiparticle fields in momentum space to translate previous treatments into a more modern form. We next develop an effective field theory describing the excitations of modes around a Fermi surface with a Van Hove singularity. We resolve lingering questions about the presence of nonlocal interactions in similar models. We find a rich and complicated theory capable of describing deviations from typical Fermi liquid behavior that nonetheless displays some universal dependence on the interactions involving modes in the vicinity of the Van Hove point. We close with an analysis of the instabilities of this Van Hove effective field theory.
" }, { "name": "Ye, Ke", "degree": "PhD", "year": "2018", "title": "A Symphony of Supersymmetry and Geometry: Invariants, Dualities and Chiral Rings", "advisor": "Gukov, Sergei", "url": "https://resolver.caltech.edu/CaltechTHESIS:05032018-153255038", "creators": [ { "name": { "family": "Ye", "given": "Ke" }, "id": "Ye-Ke", "orcid": "0000-0002-2978-2013", "display_name": "Ye, Ke" } ], "advisors": [ { "name": { "family": "Gukov", "given": "Sergei" }, "id": "Gukov-S", "orcid": "0000-0002-9486-1762", "role": "advisor", "display_name": "Gukov, Sergei" } ], "committee": [ { "name": { "family": "Schwarz", "given": "John H." }, "id": "Schwarz-J-H", "orcid": "0000-0001-9861-7559", "role": "chair", "display_name": "Schwarz, John H." }, { "name": { "family": "Wise", "given": "Mark B." }, "id": "Wise-M-B", "orcid": "0000-0002-9125-801X", "role": "member", "display_name": "Wise, Mark B." }, { "name": { "family": "Intriligator", "given": "Kenneth A." }, "id": "Intriligator-Kenneth-A", "orcid": "0000-0002-8045-1869", "role": "member", "display_name": "Intriligator, Kenneth A." }, { "name": { "family": "Gukov", "given": "Sergei" }, "id": "Gukov-S", "orcid": "0000-0002-9486-1762", "role": "member", "display_name": "Gukov, Sergei" }, { "name": { "family": "Nakayama", "given": "Yu" }, "id": "Nakayama-Yu", "orcid": "0000-0002-1747-5147", "role": "member", "display_name": "Nakayama, Yu" } ], "option_major": [ "physics" ], "doi": "10.7907/K2K2-9790", "abstract": "The present dissertation discusses aspects of supersymmetric quantum field theory, whose main themes are two-folded. First, we explore connections between superconformal theories in various dimensions and geometric invariants. Such correspondence arises from compactification of string theory or M-theory, which encodes geometric quantities into physical observables. Second, we study in detail the chiral rings and their quantum corrections in certain supersymmetric gauge theory. The goal is to shed some light on the hitherto mysterious electric-magnetic dualities.
\r\n\r\nWe first consider M5 brane on the product manifold L(k, 1) \u00d7 M3, where M3 = L(p, 1). Compactification on L(p, 1) gives rise to three dimensional theory T[L(p, 1)] whose partition function, according to 3d-3d correspondence, is equivalent to Chern-Simons invariants with complex gauge group on L(p, 1). We test the statement in Chapter 2 by taking k = 0 and calculating the supersymmetric index. We find a full agreement between two seemingly distinct quantities. In particular, when p = 1, we see the familiar S3 partition function of Chern-Simons theory arises from the index of a free theory.
\r\n\r\nWe then move on in Chapter 3 to consider M3 = S1 \u00d7 \u03a3, and twisted compactification on general Riemann surface \u03a3 with tame punctures. The twisted partition function of lens space theory T[L(k, 1)] on S1 \u00d7 \u03a3 computes the graded dimension of the Hilbert space after geometrically quantizing Hitchin moduli space MH, dubbed as \"tame Hitchin characters\" or \"equivariant Verlinde formula\". We show that this quantity can be computed from the \"Coulomb branch index\" of the class S theory T[\u03a3] on L(k, 1) \u00d7 S1. The gauge groups on two sides of the equivalence are naturally G and the Langlands dual group LG. We check explicitly the relation for G = SU(2) or SO(3). We also consider more general case where G is SU(N) or PSU(N) and show that the SU(N) equivariant Verlinde formula can be derived using field theory via (generalized) Argyres-Seiberg duality.
\r\n\r\nAs a further application, in Chapter 4 we use Coulomb branch indices of Argyres-Douglas theories on S1 \u00d7 L(k, 1) to quantize moduli spaces MH of wild/irregular Hitchin systems. We obtain the \"wild Hitchin characters\", and observe that the characters can always be written as a sum over fixed points in MH under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the vii modular transform STkS in certain vertex operator algebras. The appearance of vertex operator algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.
\r\n\r\nThe BPS spectrum of superconformal theories probe the geometry of Hitchin moduli space. Conversely, physical data of superconformal theories can be read off from Hitchin moduli space as well. We study this dictionary in Chapter 5 for general Argyres-Douglas theories and obtain a refined classification. We also discuss the S-duality of these theories, and find that the weakly coupled descriptions are given by the degeneration limit of auxiliary Riemann sphere with marked points.
\r\n\r\nFinally, in Chapter 6, we analyze classical and quantum chiral ring relations of four dimensional N = 1 adjoint SQCD with superpotential turned on for the adjoint field. In particular, for the mass deformed theory we obtain the complete on-shell vacuum expectation value for various gauge invariant chiral operators and find non trivial gaugino condensations. We argue that the solution of the chiral ring is in one-to-one correspondence with supersymmetric vacua, provided that an additional Konishi anomaly equation is included.
" }, { "name": "Pollack, Jason Aaron", "degree": "PhD", "year": "2017", "title": "Constraints on Cosmology and Quantum Gravity from Quantum Mechanics and Quantum Field Theory", "advisor": "Carroll, Sean M.", "url": "https://resolver.caltech.edu/CaltechTHESIS:05252017-171005406", "creators": [ { "name": { "family": "Pollack", "given": "Jason Aaron" }, "id": "Pollack-Jason-Aaron", "orcid": "0000-0003-4754-4905", "display_name": "Pollack, Jason Aaron" } ], "advisors": [ { "name": { "family": "Carroll", "given": "Sean M." }, "id": "Carroll-S-M", "orcid": "0000-0002-4226-5758", "role": "advisor", "display_name": "Carroll, Sean M." } ], "committee": [ { "name": { "family": "Wise", "given": "Mark B." }, "id": "Wise-M-B", "orcid": "0000-0002-9125-801X", "role": "chair", "display_name": "Wise, Mark B." }, { "name": { "family": "Carroll", "given": "Sean M." }, "id": "Carroll-S-M", "orcid": "0000-0002-4226-5758", "role": "member", "display_name": "Carroll, Sean M." }, { "name": { "family": "Cheung", "given": "Clifford W." }, "id": "Cheung-Clifford", "orcid": "0000-0002-9983-9425", "role": "member", "display_name": "Cheung, Clifford W." }, { "name": { "family": "Weinstein", "given": "Alan Jay" }, "id": "Weinstein-Alan-J-Physics", "orcid": "0000-0002-0928-6784", "role": "member", "display_name": "Weinstein, Alan Jay" } ], "option_major": [ "physics" ], "doi": "10.7907/Z9W093ZG", "abstract": "Typical cosmological states have structure, obey to very good approximation the laws of classical physics on large scales, and are far from equilibrium. Typical quantum-mechanical states have none of these properties. If the universe is described by a state in a Hilbert space, the state and its Hilbert space must therefore obey a number of constraints to describe realistic cosmological spacetimes. In particular, they must admit a quantum-to-classical transition via decoherence that allows for the emergence of classical spacetimes, and such spacetimes must obey gravitational constraints, in particular on the entanglement entropy of subsystems within them. The papers collected in this thesis are concerned with these constraints. We investigate two holographic correspondences inspired by AdS/CFT, the AdS-MERA correspondence, which suggests that anti-de~Sitter space may be given a discretized description as a tensor network, and the ER=EPR duality, which identified entangled qubits with wormholes connecting them. In the former case, we use holographic entropy bounds to severely constrain the properties of any such tensor network; in the latter case we prove a new general-relativistic area theorem which states that an area corresponding to the entanglement entropy in wormhole geometries is exactly conserved. We use information-theoretic constraints to show that under mild assumptions about the black hole interior an observer falling beyond the horizon is unable to verify the claimed cloning of information in the firewall paradox before reaching the singularity. Finally, we analyze the decoherence structures of late-time de~Sitter space and early-time slow-roll eternal inflation. We show that in the former case a universe with an infinite-dimensional Hilbert space and a positive cosmological constant inevitably reaches a maximum-entropy state from which no further branching or decoherence is possible, forbidding the existence of dynamical quantum fluctuations at late time. In the latter case, gravitational-strength interaction among inflaton modes leads to decoherence of sufficiently super-Hubble modes, which we argue backreacts to cause different histories of cosmological evolution on different branches and hence creates the conditions necessary for eternal inflation.
" } ]