De Sitter holography and entanglement entropy

A bstractWe propose a new example of entanglement knitting spacetime together, satisfying a series of checks of the corresponding von Neumann and Renyi entropies. The conjectured dual of de Sitter in d + 1 dimensions involves two coupled CFT sectors constrained by residual d-dimensional gravity. In the d = 2 case, the gravitational constraints and the CFT spectrum are relatively tractable. We identify a finite portion of each CFT Hilbert space relevant for de Sitter. Its maximum energy level coincides with the transition to the universal Cardy behavior for theories with a large central charge and a sparse light spectrum, derived by Hartman, Keller, and Stoica. Significant interactions between the two CFTs, derived previously for other reasons, suggest a maximally mixed state upon tracing out one of the two sectors; we derive this by determining the holographic Renyi entropies. The resulting entanglement entropy matches the Gibbons-Hawking formula for de Sitter entropy, including the numerical coefficient. Finally, we interpret the Gibbons-Hawking horizon entropy in terms of the Ryu-Takayanagi entropy, and explore the time evolution of the entanglement entropy.

[1]  S. S. Strogalov.  ON POINCARÉ SERIES , 1978 .

[2]  Matthew B Hastings,et al.  Area laws in quantum systems: mutual information and correlations. , 2007, Physical review letters.

[3]  T. Takayanagi,et al.  Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence. , 2006, Physical review letters.

[4]  I. Klebanov,et al.  Entanglement as a probe of confinement , 2007, 0709.2140.

[5]  M. Raamsdonk,et al.  Comments on quantum gravity and entanglement , 2009, 0907.2939.

[6]  Xi Dong,et al.  FRW Solutions and Holography from Uplifted AdS/CFT , 2012 .

[7]  Matthew Headrick,et al.  Entanglement Renyi entropies in holographic theories , 2010, 1006.0047.

[8]  Andrew Strominger.  The dS/CFT correspondence , 2001 .

[9]  D. Stanford,et al.  Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT , 2011, 1104.2621.

[10]  S. Shenker,et al.  Multiple shocks , 2013, 1312.3296.

[11]  S. Dimopoulos,et al.  Generating Small Numbers by Tunneling in Multi-Throat Compactifications , 2004 .

[12]  L. Randall,et al.  An Alternative to compactification , 1999, hep-th/9906064.

[13]  Holographic framework for eternal inflation , 2006, hep-th/0606204.

[14]  J. Cardy.  The $T\overline T$ deformation of quantum field theory as a stochastic process , 2018 .

[15]  Aron C. Wall,et al.  Traversable wormholes via a double trace deformation , 2016, Journal of High Energy Physics.

[16]  D. Marolf,et al.  Complex entangling surfaces for AdS and Lifshitz black holes? , 2014, 1407.2900.

[17]  S. Hawking,et al.  Cosmological Event Horizons, Thermodynamics, and Particle Creation , 1977 .

[18]  L. Susskind,et al.  Two-dimensional quantum cosmology. , 1991 .

[19]  T. Takayanagi,et al.  Surface/State Correspondence as a Generalized Holography , 2015, 1503.03542.

[20]  H. Verlinde,et al.  Moving the CFT into the bulk with TT¯$$ T\overline{T} $$ , 2018 .

[21]  J. Maldacena,et al.  Eternal black holes in anti-de Sitter , 2001, hep-th/0106112.

[22]  C. Keller,et al.  Universal spectrum of 2d conformal field theory in the large c limit , 2014, 1405.5137.

[23]  William Cottrell,et al.  Comments on TT¯ double trace deformations and boundary conditions , 2018, Physics Letters B.

[24]  J. Camps.  Generalized entropy and higher derivative gravity , 2013, 1310.6659.

[25]  J. Polchinski.  A two-dimensional model for quantum gravity , 1989 .

[26]  S. Hellerman.  A universal inequality for CFT and quantum gravity , 2009, 0902.2790.

[27]  Xi Dong,et al.  Bulk locality and quantum error correction in AdS/CFT , 2014, 1411.7041.

[28]  C. Closset,et al.  N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model , 2017, 1707.05774.

[29]  Xi Dong,et al.  Moduli stabilization and the holographic RG for AdS and dS , 2013, Journal of High Energy Physics.

[30]  T. Takayanagi,et al.  Entanglement between two interacting CFTs and generalized holographic entanglement entropy , 2014, 1403.1393.

[31]  D. Marolf,et al.  Cutoff AdS3 versus the TT¯$$ T\overline{T} $$ deformation , 2018, Journal of High Energy Physics.

[32]  Y. Sato.  Comments on Entanglement Entropy in the dS/CFT Correspondence , 2015, 1501.04903.

[33]  Xi Dong,et al.  Micromanaging de Sitter holography , 2010, 1005.5403.

[34]  Y. Nomura,et al.  Spacetime from unentanglement , 2017, 1711.05263.

[35]  Xi Dong.  The gravity dual of Rényi entropy , 2016, Nature Communications.

[36]  C. Keller,et al.  Poincaré series, 3D gravity and CFT spectroscopy , 2014, 1407.6008.

[37]  L. Susskind,et al.  Cool horizons for entangled black holes , 2013, 1306.0533.

[38]  Raphael Bousso.  Positive vacuum energy and the N-bound , 2000 .

[39]  H. Verlinde,et al.  Moving the CFT into the bulk with TT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ T\overline{T} $$\end{document} , 2016, Journal of High Energy Physics.

[40]  M. Raamsdonk,et al.  Momentum-space entanglement and renormalization in quantum field theory , 2011, 1108.3568.

[41]  K. Narayan.  Extremal surfaces in de Sitter spacetime , 2015 .

[42]  Dionysios Anninos.  DE SITTER MUSINGS , 2012, 1205.3855.

[43]  Edward Witten.  Anti-de Sitter Space, Thermal Phase Transition, And Confinement in Gauge Theories , 1998 .

[44]  D. Marolf,et al.  Cutoff AdS 3 versus the T T deformation , 2018 .

[45]  T. Banks.  Cosmological breaking of supersymmetry , 2000 .

[46]  E. Martinec,et al.  Closed string tachyon condensation and worldsheet inflation , 2003, hep-th/0303087.

[47]  T. Takayanagi,et al.  Holographic Derivation of Entanglement Entropy from AdS/CFT , 2006, hep-th/0603001.

[48]  E. Silverstein,et al.  Varying dilaton as a tracer of classical string interactions , 2017, 1704.02625.

[49]  Xi Dong,et al.  Holographic entanglement entropy for general higher derivative gravity , 2013, 1310.5713.

[50]  A. Mollabashi,et al.  Entanglement in Lifshitz-type quantum field theories , 2017, 1705.00483.

[51]  P. Hayden,et al.  Holographic duality from random tensor networks , 2016, 1601.01694.

[52]  Xiao-Liang Qi,et al.  Eternal traversable wormhole , 2018, 1804.00491.

[53]  K. Narayan.  On extremal surfaces and de Sitter entropy , 2017, 1711.01107.

[54]  Aitor Lewkowycz,et al.  Generalized gravitational entropy , 2013, 1304.4926.

[55]  The dS/dS Correspondence , 2004, hep-th/0407125.

[56]  M. Smedbäck.  Pulsating strings on Ads(5) x S(5) , 2004 .

[57]  Miranda C. N. Cheng,et al.  Elliptic Genera and 3d Gravity , 2015, 1503.04800.

[58]  J. Preskill,et al.  Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence , 2015, 1503.06237.

[59]  L. Susskind,et al.  The Holographic bound in anti-de Sitter space , 1998, hep-th/9805114.

[60]  S. Dubovsky,et al.  Asymptotic fragility, near AdS2 holography and TT¯$$ T\overline{T} $$ , 2017, 1706.06604.

[61]  J. Maldacena.  Non-Gaussian features of primordial fluctuations in single field inflationary models , 2002, astro-ph/0210603.

[62]  E. Silverstein.  TASI lectures on cosmological observables and string theory , 2016, 1606.03640.

[63]  M. Mozaffar,et al.  On the entanglement between interacting scalar field theories , 2015, 1509.03829.

[64]  T. Takayanagi,et al.  A covariant holographic entanglement entropy proposal , 2007, 0705.0016.

[65]  Riccardo D'Auria,et al.  KK Spectroscopy of Type IIB Supergravity on $AdS_{5} \times T^{11}$ , 1999 .

[66]  Zhenbin Yang,et al.  Diving into traversable wormholes , 2017, 1704.05333.

[67]  Thomas Hartman,et al.  Higher spin realization of the DS/CFT correspondence , 2011, 1108.5735.

[68]  R. Bousso.  A covariant entropy conjecture , 1999, hep-th/9905177.

[69]  A. Karch,et al.  Holographic entanglement entropy and the internal space , 2014, 1501.00003.

[70]  S. Dimopoulos,et al.  Small Numbers From Tunneling Between Brane Throats , 2001 .