Holography Beyond Ads/CFT by Nicholas S Salzetta a Dissertation

Total Page:16

File Type:pdf, Size:1020Kb

Holography Beyond Ads/CFT by Nicholas S Salzetta a Dissertation Holography beyond AdS/CFT by Nicholas S Salzetta Adissertationsubmittedinpartialsatisfactionofthe requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Yasunori Nomura, Chair Professor Ori Ganor Assistant Professor Jessica Lu Fall 2019 Holography beyond AdS/CFT Copyright 2019 by Nicholas S Salzetta 1 Abstract Holography beyond AdS/CFT by Nicholas S Salzetta Doctor of Philosophy in Physics University of California, Berkeley Professor Yasunori Nomura, Chair Physicists have long sought to fully understand how gravity can be fully formulated within aquantummechanicalframework.Apromisingavenueofresearchinthisdirectionwas born from the idea of holography - that gravitational physics can be recast as a di↵erent theory living in fewer dimensions. Evidence of this phenomena was first observed in the arena of black hole physics, where the entropy of a black hole was calculated to scale with its area, not its volume. The advent of the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence provided an explicit realization of holography for gravitational theories in AdS space. This brought a flurry of activity dedicated to dissecting this correspondence. Ultimately, however, it will be necessary to move beyond the confines of AdS/CFT in order to understand our universe, as we live in a de Sitter type universe. The research presented in this dissertation attempts to broaden the scope of holgraphic theories to include more phenomenologically relevant universes. To do so, we utilize a top-down approach and take results from AdS/CFT that appear to be general holographic results and see how they can be applied in spacetimes other than AdS. In particular, we take the Ryu-Takayanagi (RT) formula, along with its related results, and investigate what we can learn by applying it to general spacetimes. Doing so naturally forces us to utilize holographic screens, as these are the largest such surfaces where the RT formula can be self-consistently applied. This approach allows us to examine properties of the purported boundary theory for general spacetimes, including the entanglement structure and propagation speeds of excitations dual to bulk excitations. This is done in chapters 2 and 3. In chapters 4 and 5, we use this lens of generalized holography to elucidate the nature of the relationship between entanglement and emergent geometry. Finally, in chapter 6, we revisit one the important underlying assumption that the RT formula is general and demonstrate the validity of this assumption. i To my parents, Meg and Paul ii Contents Contents ii List of Figures iv 1 Introduction 1 2 Toward holography for general spacetimes 6 2.1 Introduction . 6 2.2 HolographyandQuantumGravity. 10 2.3 HolographicDescriptionofFRWUniverses . 14 2.4 Interpretation:BeyondAdS/CFT . 27 2.5 Discussion . 42 2.6 Appendix ..................................... 48 3 Butterfly Velocities for Holographic Theories of General Spacetimes 55 3.1 Introduction . 55 3.2 Definition of the Butterfly Velocity in Holographic Theories of General Space- times . 56 3.3 Butterfly Velocities for the Holographic Theory of FRW Universes . 60 3.4 Discussion . 65 4 Spacetime from Unentanglement 67 4.1 Introduction . 67 4.2 MaximallyEntropicStatesHaveNoSpacetime. 69 4.3 Spacetime Emerges through Deviations from Maximal Entropy . 84 4.4 HolographicHilbertSpaces. 90 4.5 Conclusion . 93 4.6 Appendix ..................................... 99 5 Pulling the Boundary into the Bulk 113 5.1 Introduction . 113 5.2 Motivation . 116 5.3 HolographicSlice ................................. 117 iii 5.4 Examples . 122 5.5 InterpretationandApplications . 130 5.6 Relationship to Renormalization . 137 5.7 Discussion . 139 5.8 Appendix ..................................... 141 6 HolographicEntanglementEntropyinTTDeformedCFTs 148 6.1 Introduction . 148 6.2 FieldTheoryCalculation. 149 6.3 Bulk Calculation . 153 6.4 Discussion . 154 Bibliography 157 iv List of Figures 2.1 For a fixed semiclassical spacetime, the holographic screen is a hypersurface ob- tained as the collection of codimension-2 surfaces (labeled by ⌧)onwhichthe expansion of the light rays emanating from a timelike curve p(⌧)vanishes,✓ =0. This way of erecting the holographic screen automatically deals with the redun- dancy associated with complementarity. The ambiguity of choosing p(⌧)reflects alargefreedominfixingtheredundancyassociatedwithholography. 11 2.2 The congruence of past-directed light rays emanating from p0 (the origin of the reference frame) has the largest cross sectional area on a leaf σ,wheretheholo- graphic theory lives. At any point on σ,therearetwofuture-directednullvectors orthogonal to the leaf: ka and la.ForagivenregionΓoftheleaf,wecanfinda codimension-2 extremal surface E(Γ) anchored to the boundary @ΓofΓ,which is fully contained in the causal region Dσ associated with σ............ 13 2.3 Various FRW universes, I, II, III, ,havethesameboundaryarea at di↵erent ⇤ times, t (I),t (II),t (III), .Quantumstatesrepresentinguniversesatthese··· A ⇤ ⇤ ⇤ moments belong to Hilbert··· space specified by the value of the boundary area. 16 ⇤ 2.4 A region L(γ)oftheleafσ is parameterizedH by an angle γ :[0,⇡]. The extremal ⇤ surface E(γ)anchoredtoitsboundary,@L(γ), is also depicted schematically. (In fact, E(γ)bulgesintothetimedirection.) . 17 2.5 The value of Q(γ)asafunctionofγ (0 γ ⇡/2) for w = 1(vacuumenergy), 0.98, 0.8, 0 (matter), 1/3 (radiation), and 1. The dotted− line indicates the lower− bound− given by the flat space geometry, which can be realized in a curvature dominatedopenFRWuniverse. 20 2.6 The value of Q(⇡/2) as a function of w.......................21 2.7 The shape of the extremal surfaces E(⇡/2) for w = 1, 0.98, 0.8, 0, 1/3, and 1. The horizontal axis is the cylindrical radial coordinate− − normalized− by the apparent horizon radius, ⇠/⇠AH, and the vertical axis is the Hubble time, tH... 22 2.8 An FRW universe whose dominant component changes from w to w0 at time t0. Two surfaces depicted by orange lines are the latest extremal surface fully con- tained in the w region (bottom) and the earliest extremal surface fully contained in the w0 region (top), each anchored to the leaves at t and t0.. 25 ⇤ v 2.9 The ratio of the screen entanglement entropies, Rw = R1w(⇡/2), before and after the transition from a universe with the equation of state parameter w to that with w0 = 1, obtained from Figs. 2.6 and 2.7 using Eq. (2.58). The dot at w = 1 − represents R 1 = R1 1(⇡/2) obtained in Eq. (2.59). 26 − − 2.10 A steep potential (a) leading to the time evolution of the scalar field (b), the area of a leaf hemisphere (c), and the screen entanglement entropy (d). The same for abroadpotential(e)–(h). 28 2.11 Possible structures of the Hilbert space for a fixed boundary space B.In H⇤ the direct sum structure (left), each semiclassical spacetime in Dσ has its own ⇤ Hilbert space ,w.TheRussiandollstructure(right)correspondstothesce- ⇤ nario of “spacetimeH equals entanglement,” i.e. the entanglement entropies of the holographic degrees of freedom determine spacetime in Dσ .Thisimpliesthata ⇤ superposition of exponentially many semiclassical spacetimes can lead to a dif- ferent semiclassical spacetime. 31 2.12 If a black hole forms inside the holographic screen, future-directed ingoing light rays emanating orthogonally from the leaf σ at an intermediate time may hit the ⇤ singularity before reaching a caustic. While the diagram here assumes spherical symmetry for simplicity, the phenomenon can occur more generally. 36 2.13 To determine a state in the future, we need information on the “exterior” light sheet, the light sheet generated by light rays emanating from σ in the ka ⇤ directions, in addition to that on the “interior” light sheet, i.e. the one generated− by light rays emanating in the +ka directions. 37 2.14 In a universe beginning with a big bang, obtaining a future state requires a spec- ification of signals from the big bang singularity, in addition to the information contained in the original state. In an FRW universe this is done by imposing spa- tial homogeneity and isotropy, which corresponds to selecting a fine-tuned state from the viewpoint of the big bang universe. 43 3.1 A local operator at p, represented by the dot, is on the HRT surface anchored to the boundary of a spherical cap region, 0 γ,ontheleafattime⌘ ,located ⇤ at r = r . Note that the figure suppresses the time direction; for example, the ⇤ operator is not at the same time as the leaf. 61 3 3.2 Butterfly velocity vB multiplied by γ as a function of f. Here, γ is the angular size of the leaf region, and f is the fractional displacement of the bulk local operatorfromthetipoftheHRTsurface;seeEq.(3.15). 63 3.3 Butterfly velocity vB of a bulk local operator at the tip of the HRT surface, f =0,asafunctionoftheangularsizeγ of the leaf region for w =1,1/3, 0, 1/3, and 2/3 (solid curves, from top to bottom). The dashed curve represents − 3− vB =4/3γ ,theanalyticresultobtainedforγ 1inEq.(3.31).Thehorizontal dashed line represents the speed of light. .⌧ . 65 vi 4.1 The volume V (r+,R) of the Schwarzschild-AdS spacetime that can be recon- structed from the boundary theory, normalized by the corresponding volume V (R) in empty AdS space: f = V (r+,R)/V (R). Here, R is the infrared cut- o↵of (d + 1)-dimensional AdS space, and r+ is the horizon radius of the black hole. 73 4.2 The Penrose diagram of de Sitter space. The spacetime region covered by the flat- slicing coordinates is shaded, and constant time slices in this coordinate system are drawn. The codimension-1 null hypersurface ⌃0 is the cosmological horizon for an observer at r = 0, to which the holographic screen of the FRW universe asymptotes in the future. 75 4.3 Constant time slices and the spacetime region covered by the coordinates in static slicing of de Sitter space.
Recommended publications
  • States with Regards to Finding If the Cosmological Constant Is, Or Is Not a ‘Vacuum’ Field Andrew Beckwith, [email protected]
    Consequences of squeezing initially coherent (semi classical) states with regards to finding if the cosmological constant is, or is not a ‘vacuum’ field Andrew Beckwith, [email protected], Abstract The following document is to prepare an analysis on if the cosmological constant is a vacuum field. Candidates for how to analyze this issue come up in terms of brane theory, modified treatments of WdM theory (pseudo time component added) and/ or how to look at squeezing of vacuum states, as initially coherent semi classical constructions, or string theory versions of coherent states. The article presents a thought experiment if there is a non zero graviton mass, and at the end, in the conclusion states experimental modeling criteria which may indicate if a non zero graviton mass is measurable, which would indicate the existence, de facto of a possible replacement for DE, based upon non zero mass gravitons, and indications for a replacement for a cosmological constant. Introduction: Dr. Karim1 mailed the author with the following question which will be put in quotes: The challenge of resolving the following question: At the Big Bang the only form of energy released is in the form of geometry – gravity. intense gravity field lifts vacuum fields to positive energies, So an electromagnetic vacuum of density 10122 kg/m3 should collapse under its own gravity. But this does not happen - that is one reason why the cosmological constant cannot be the vacuum field. Why? Answering this question delves into what the initial state of the universe should be, in terms of either vacuum energy, or something else.
    [Show full text]
  • Spacetime Geometry from Graviton Condensation: a New Perspective on Black Holes
    Spacetime Geometry from Graviton Condensation: A new Perspective on Black Holes Sophia Zielinski née Müller München 2015 Spacetime Geometry from Graviton Condensation: A new Perspective on Black Holes Sophia Zielinski née Müller Dissertation an der Fakultät für Physik der Ludwig–Maximilians–Universität München vorgelegt von Sophia Zielinski geb. Müller aus Stuttgart München, den 18. Dezember 2015 Erstgutachter: Prof. Dr. Stefan Hofmann Zweitgutachter: Prof. Dr. Georgi Dvali Tag der mündlichen Prüfung: 13. April 2016 Contents Zusammenfassung ix Abstract xi Introduction 1 Naturalness problems . .1 The hierarchy problem . .1 The strong CP problem . .2 The cosmological constant problem . .3 Problems of gravity ... .3 ... in the UV . .4 ... in the IR and in general . .5 Outline . .7 I The classical description of spacetime geometry 9 1 The problem of singularities 11 1.1 Singularities in GR vs. other gauge theories . 11 1.2 Defining spacetime singularities . 12 1.3 On the singularity theorems . 13 1.3.1 Energy conditions and the Raychaudhuri equation . 13 1.3.2 Causality conditions . 15 1.3.3 Initial and boundary conditions . 16 1.3.4 Outlining the proof of the Hawking-Penrose theorem . 16 1.3.5 Discussion on the Hawking-Penrose theorem . 17 1.4 Limitations of singularity forecasts . 17 2 Towards a quantum theoretical probing of classical black holes 19 2.1 Defining quantum mechanical singularities . 19 2.1.1 Checking for quantum mechanical singularities in an example spacetime . 21 2.2 Extending the singularity analysis to quantum field theory . 22 2.2.1 Schrödinger representation of quantum field theory . 23 2.2.2 Quantum field probes of black hole singularities .
    [Show full text]
  • The Anthropic Principle and Multiple Universe Hypotheses Oren Kreps
    The Anthropic Principle and Multiple Universe Hypotheses Oren Kreps Contents Abstract ........................................................................................................................................... 1 Introduction ..................................................................................................................................... 1 Section 1: The Fine-Tuning Argument and the Anthropic Principle .............................................. 3 The Improbability of a Life-Sustaining Universe ....................................................................... 3 Does God Explain Fine-Tuning? ................................................................................................ 4 The Anthropic Principle .............................................................................................................. 7 The Multiverse Premise ............................................................................................................ 10 Three Classes of Coincidence ................................................................................................... 13 Can The Existence of Sapient Life Justify the Multiverse? ...................................................... 16 How unlikely is fine-tuning? .................................................................................................... 17 Section 2: Multiverse Theories ..................................................................................................... 18 Many universes or all possible
    [Show full text]
  • Arxiv:Hep-Th/0209231 V1 26 Sep 2002 Tbs,Daai N Uigi Eurdfrsae Te Hntetemlvcu Olead to Vacuum Thermal the Anisotropy
    SLAC-PUB-9533 BRX TH-505 October 2002 SU-ITP-02/02 Initial conditions for inflation Nemanja Kaloper1;2, Matthew Kleban1, Albion Lawrence1;3;4, Stephen Shenker1 and Leonard Susskind1 1Department of Physics, Stanford University, Stanford, CA 94305 2Department of Physics, University of California, Davis, CA 95616 3Brandeis University Physics Department, MS 057, POB 549110, Waltham, MA 02454y 4SLAC Theory Group, MS 81, 2575 Sand Hill Road, Menlo Park, CA 94025 Free scalar fields in de Sitter space have a one-parameter family of states invariant under the de Sitter group, including the standard thermal vacuum. We show that, except for the thermal vacuum, these states are unphysical when gravitational interactions are arXiv:hep-th/0209231 v1 26 Sep 2002 included. We apply these observations to the quantum state of the inflaton, and find that at best, dramatic fine tuning is required for states other than the thermal vacuum to lead to observable features in the CMBR anisotropy. y Present and permanent address. *Work supported in part by Department of Energy Contract DE-AC03-76SF00515. 1. Introduction In inflationary cosmology, cosmic microwave background (CMB) data place a tanta- lizing upper bound on the vacuum energy density during the inflationary epoch: 4 V M 4 1016 GeV : (1:1) ∼ GUT ∼ Here MGUT is the \unification scale" in supersymmetric grand unified models, as predicted by the running of the observed strong, weak and electromagnetic couplings above 1 T eV in the minimal supersymmetric standard model. If this upper bound is close to the truth, the vacuum energy can be measured directly with detectors sensitive to the polarization of the CMBR.
    [Show full text]
  • The Multiverse: Conjecture, Proof, and Science
    The multiverse: conjecture, proof, and science George Ellis Talk at Nicolai Fest Golm 2012 Does the Multiverse Really Exist ? Scientific American: July 2011 1 The idea The idea of a multiverse -- an ensemble of universes or of universe domains – has received increasing attention in cosmology - separate places [Vilenkin, Linde, Guth] - separate times [Smolin, cyclic universes] - the Everett quantum multi-universe: other branches of the wavefunction [Deutsch] - the cosmic landscape of string theory, imbedded in a chaotic cosmology [Susskind] - totally disjoint [Sciama, Tegmark] 2 Our Cosmic Habitat Martin Rees Rees explores the notion that our universe is just a part of a vast ''multiverse,'' or ensemble of universes, in which most of the other universes are lifeless. What we call the laws of nature would then be no more than local bylaws, imposed in the aftermath of our own Big Bang. In this scenario, our cosmic habitat would be a special, possibly unique universe where the prevailing laws of physics allowed life to emerge. 3 Scientific American May 2003 issue COSMOLOGY “Parallel Universes: Not just a staple of science fiction, other universes are a direct implication of cosmological observations” By Max Tegmark 4 Brian Greene: The Hidden Reality Parallel Universes and The Deep Laws of the Cosmos 5 Varieties of Multiverse Brian Greene (The Hidden Reality) advocates nine different types of multiverse: 1. Invisible parts of our universe 2. Chaotic inflation 3. Brane worlds 4. Cyclic universes 5. Landscape of string theory 6. Branches of the Quantum mechanics wave function 7. Holographic projections 8. Computer simulations 9. All that can exist must exist – “grandest of all multiverses” They can’t all be true! – they conflict with each other.
    [Show full text]
  • SUPERSYMMETRIC UNIFICATION Savas Dimopoulos+
    CERN-TH.7531/94 ) SUPERSYMMETRIC UNIFICATION +) Savas Dimop oulos Theoretical Physics Division, CERN CH - 1211 Geneva23 ABSTRACT The measured value of the weak mixing angle is, at present, the only precise exp erimental indication for physics b eyond the Standard Mo del. It p oints in the direction of Uni ed Theo- ries with Sup ersymmetric particles at accessible energies. We recall the ideas that led to the construction of these theories in 1981. Talk presented at the International Conference on the History of Original Ideas and Basic Discoveries in Particle Physics held at Ettore Ma jorana Centre for Scienti c Culture, Erice, Sicily, July 29-Aug.4 1994. CERN-TH.7531/94 Decemb er 1994 1 Why Sup ersymmetric Uni cation? It is a pleasure to recall the ideas that led to the rst Sup ersymmetric Uni ed Theory and its low energy manifestation, the Sup ersymmetric SU (3) SU (2) U (1) mo del. This theory synthesizes two marvelous ideas, Uni cation [1] and Sup ersymmetry [2, 3 ]. The synthesis is catalyzed by the hierarchy problem [4] which suggests that Sup ersymmetry o ccurs at accessible energies [5]. Since time is short and we are explicitly asked to talk ab out our own contributions I will not cover these imp ortant topics. A lo ok at the the program of this Conference reveals that most other topics covered are textb o ok sub jects, such as Renormalization of the Standard Mo del [6] and Asymptotic Free- dom [7], that are at the foundation of our eld. So it is natural to ask why Sup ersymmetric Uni cation is included in such a distinguished companyofwell-established sub jects? I am not certain.
    [Show full text]
  • PDF Download the Black Hole War : My Battle with Stephen Hawking To
    THE BLACK HOLE WAR : MY BATTLE WITH STEPHEN HAWKING TO MAKE THE WORLD SAFE FOR QUANTUM MECHANICS PDF, EPUB, EBOOK Leonard Susskind | 480 pages | 05 Nov 2009 | Little, Brown & Company | 9780316016414 | English | New York, United States The Black Hole War : My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics PDF Book Black Holes and Quantum Physics. Softcover edition. Most scientists didn't recognize the import of Hawking's claims, but Leonard Susskind and Gerard t'Hooft realized the threat, and responded with a counterattack that changed the course of physics. Please follow the detailed Help center instructions to transfer the files to supported eReaders. The Black Hole War is the thrilling story of their united effort to reconcile Hawking's theories of black holes with their own sense of reality, an effort that would eventually result in Hawking admitting he was wrong and Susskind and 't Hooft realizing that our world is a hologram projected from the outer boundaries of space. This is the inside account of the battle over the true nature of black holes—with nothing less than our understanding of the entire universe at stake. From the bestselling author of The White Donkey, a heartbreaking and visceral graphic novel set against the stark beauty of Afghanistan's mountain villages that examines prejudice and the military remnants of colonialism. Most scientists didn't recognize the import of Hawking's claims, but Leonard Susskind and Gerard t'Hooft realized the threat, and responded with a counterattack that changed the course of physics. But really, unlike it sounds, this means that information, or characteristics of an object, must always be preserved according to classical physics theory.
    [Show full text]
  • Generalizing Entropic Force Formalism
    Yongpyung 2012, Greenpia Condo, Feb. 21st 2012 GENERALIZING ENTROPIC FORCE FORMALISM Jin-Ho Cho (Hanyang University) w/ Hosin Gong, Hyosung Kim (POSTECH) Motivation (for the entropic force) Quantum Gravity .....not successful so far the role of gravity in AdS/CFT tree level supergravity (closed string) / quantum SYM (open string) Fundamental or Emergent? Entropic Force rubber band tends to increase the entropy S : larger S : smaller [Halliday et al., Fundamentals of Physics] Verlinde’s Idea [Erik Verlinde, 1001.0785] entropic force : F x = T S 4 4 3 holographic principle : Ac /G~ = N E = NkBT/2 T = ~a/2πkBc entropy change : S =2πkB( x mc/~) 4 4 (for a screen shift x ) 4 Newtonian Physics Newton’s law : (a planar screen) T = ~a/2πckB S =2πkB( x mc/~) 4 4 F x = T S 4 4 ~a 2πkBmc x = 4 2πk c ✓ B ◆✓ ~ ◆ = ma x 4 3 Gravitational force : (a spherical screen) N = Ac /G~ 2 Mc = E = NkBT/2 1 Ac3 ~a r2c2 = = a 2 G 2πc ✓ ~ ◆✓ ◆ G Q1: Cosmological Constant ? g R ab R + ⇤g =8⇡GT ab − 2 ab ab 3 Ac /G~ = N F x = T S S =2πkB( x mc/~) 4 4 E = NkBT/2 4 4 T = ~a/2πkBc ‘Volume Energy’ NkBT E = Mc2 +↵V = 2 N~ a ~a = T = 4⇡c 2⇡ckB 2 Ac a 3 = N = Ac /G~ 4⇡G 4⇡GM 4⇡G↵V a = + A Ac2 Determination of ↵ spherically symmetric case GM 4⇡G↵r a = + = Φ r2 3c2 r GM c2⇤r = Newtonian limit of Einstein eq. r2 − 3 c4 ↵ = ⇤ −4⇡G Einstein equation 4 c NkBT E = Mc2 ⇤V = − 4⇡G 2 c4 k c3 Mc2 ⇤ dV = B TdN = adA − 4⇡G 2 4⇡G Z Z Z 1 a b 1 a b 2 T Tg n ⇠ dV ⇤gabn ⇠ dV ab − 2 ab −4⇡G Z⌃ ✓ ◆ Z⌃ 1 = R na⇠b dV 4⇡G ab Z⌃ Q2: Entropic Coulomb Force ? [JHC & Hyosung Kim, 2012 J.
    [Show full text]
  • Curriculum Vitae
    SEBASTIAN DE HARO Curriculum Vitae Assistant Professor in Philosophy of Science at the Institute for Logic, Language and Computation and the Institute of Physics of the University of Amsterdam 1. RESEARCH PROFILE Areas of specialisation: Philosophy of Science, History and Philosophy of Physics, Theoretical Physics Areas of competence: Epistemology, Metaphysics, Ethics, Philosophical and Social Aspects of Information, History of Science, History of Philosophy, Philosophy of Logic and Language, Philosophy of Mathematics 2. PREVIOUS POSITIONS • Lecturer (2009-2020), Amsterdam University College (AUC), University of Amsterdam. Tasks: teaching, curriculum development and evaluation, thesis supervision, member of the BSA committee. Between 2009-2015 I also had tutoring responsibilities. • Lecturer (2019-2020, fixed term), Department of Philosophy, Free University Amsterdam • Lecturer in theoretical physics (fixed term), Institute for Theoretical Physics, Faculty of Science, University of Amsterdam. Teaching, research, thesis supervision. 02/12 - 07/14. • Research associate. Managing editor of Foundations of Physics on behalf of Gerard ’t Hooft, Spinoza Institute/ITP, Utrecht University and Springer Verlag, 2008-2009. Research, managing editorial office, setting up new projects, contact Editorial Board. 3. PUBLICATIONS Total number of citations (all publications): 2,751. i10-index: 33. h-index: 22 Full list of publications and citation information via Google scholar profile: http://scholar.google.nl/citations?user=rmXDqN4AAAAJ&hl=nl&oi=ao Journal articles, book chapters, and book reviews General philosophy of science: journal articles (6) 1. ‘The Empirical Under-determination Argument Against Scientific Realism for Dual Theories’. Erkenntnis, 2021. https://link.springer.com/article/10.1007%2Fs10670-020-00342-0 2. ‘Science and Philosophy: A Love-Hate Relationship’.
    [Show full text]
  • Supersymmetry at Large Distance Scales
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server PUPT-1925 Supersymmetry at Large Distance Scales Herman Verlinde Physics Department, Princeton University, Princeton, NJ 08544 Abstract We propose that the UV/IR relation that underlies the AdS/CFT duality may provide a natural mechanism by which high energy supersymmetry can have large distance conse- quences. We motivate this idea via (a string realization of) the Randall-Sundrum scenario, in which the observable matter is localized on a matter brane separate from the Planck brane. As suggested via the holographic interpretation of this scenario, we argue that the local dynamics of the Planck brane – which determines the large scale 4-d geometry – is protected by the high energy supersymmetry of the dual 4-d theory. With this assumption, we show that the total vacuum energy naturally cancels in the effective 4-d Einstein equa- tion. This cancellation is robust against changes in the low energy dynamics on the matter brane, which gets stabilized via the holographic RG without any additional fine-tuning. 1. Introduction The observed smallness of the cosmological constant requires a remarkable cancellation of all vacuum energy contributions [1]. Supersymmetry seems at present the only known symmetry that could naturally explain this cancellation, but thus far no mechanism for supersymmetry breaking is known that would not destroy this property. Nonetheless, in searching for a possible resolution of the cosmological constant problem, it seems natural to include supersymmetry as a central ingredient. What would then be needed, however, is a mechanism – some UV/IR correspondence – by which the short distance cancellations of supersymmetry can somehow be translated into a long distance stability of the cosmological evolution equations.
    [Show full text]
  • A Unitary S-Matrix for 2D Black Hole Formation and Evaporation
    PUPT-1380 IASSNS-HEP-93/8 February 1993 A Unitary S-matrix for 2D Black Hole Formation and Evaporation Erik Verlinde School of Natural Sciences Institute for Advanced Study Princeton, NJ 08540 and Herman Verlinde Joseph Henry Laboratories Princeton University Princeton, NJ 08544 arXiv:hep-th/9302022v1 7 Feb 1993 Abstract We study the black hole information paradox in the context of a two-dimensional toy model given by dilaton gravity coupled to N massless scalar fields. After making the model well-defined by imposing reflecting boundary conditions at a critical value of the dilaton field, we quantize the theory and derive the quantum S-matrix for the case that N=24. This S-matrix is unitary by construction, and we further argue that in the semiclassical regime it describes the formation and subsequent Hawking evaporation of two-dimensional black holes. Finally, we note an interesting correspondence between the dilaton gravity S-matrix and that of the c = 1 matrix model. 1. Introduction The discovery that black holes can evaporate by emitting thermal radiation has led to a longstanding controversy about whether or not quantum coherence can be maintained in this process. Hawking’s original calculation [1] suggests that an initial state, describing matter collapsing into a black hole, will eventually evolve into a mixed state describing the thermal radiation emitted by the black hole. The quantum physics of black holes thus seems inherently unpredictable. However, this is clearly an unsatisfactory conclusion, and several attempts have been made to find a description of black hole evaporation in accordance with the rules of quantum mechanics [2, 3], but so far all these attempts have run into serious difficulties.
    [Show full text]
  • Thesis in Amsterdam
    UvA-DARE (Digital Academic Repository) The physics and mathematics of microstates in string theory: And a monstrous Farey tail de Lange, P. Publication date 2016 Document Version Final published version Link to publication Citation for published version (APA): de Lange, P. (2016). The physics and mathematics of microstates in string theory: And a monstrous Farey tail. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:10 Oct 2021 P a u A dissertation that delves l The Physics & d into physical and e L mathematical aspects of a Microstates Mathematics of n g string theory. In the first e part ot this book, Microstates in T microscopic porperties of h Moonshine e string theoretic black String Theory P h holes are investigated.
    [Show full text]