Abstract
The \( T\overline{T} \) deformation of a conformal field theory has a dual description as a cutoff AdS3 spacetime, at least at the level of pure 3d gravity. We generalize this deformation in such a way that it builds up a patch of bulk dS3 spacetime instead. At each step along the trajectory in the space of 2d theories, the theory is deformed by a specific combination of \( T\overline{T} \) and the two-dimensional cosmological constant. This provides a concrete holographic dual for the warped throat on the gravity side of the dS/dS duality, at leading order in large central charge. We also analyze a sequence of excitations of this throat on both sides of the duality, as well as the entanglement entropy. Our results point toward a mechanism for obtaining de Sitter solutions starting from seed conformal field theories with AdS duals.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Anninos, De Sitter musings, Int. J. Mod. Phys. A 27 (2012) 1230013 [arXiv:1205.3855] [INSPIRE].
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].
A. Strominger, Inflation and the dS/CFT correspondence, JHEP 11 (2001) 049 [hep-th/0110087] [INSPIRE].
M. Alishahiha, A. Karch, E. Silverstein and D. Tong, The dS/dS correspondence, AIP Conf. Proc. 743 (2004) 393 [hep-th/0407125] [INSPIRE].
M. Alishahiha, A. Karch and E. Silverstein, Hologravity, JHEP 06 (2005) 028 [hep-th/0504056] [INSPIRE].
B. Freivogel, Y. Sekino, L. Susskind and C.-P. Yeh, A holographic framework for eternal inflation, Phys. Rev. D 74 (2006) 086003 [hep-th/0606204] [INSPIRE].
X. Dong, B. Horn, E. Silverstein and G. Torroba, Micromanaging de Sitter holography, Class. Quant. Grav. 27 (2010) 245020 [arXiv:1005.5403] [INSPIRE].
X. Dong et al., FRW solutions and holography from uplifted AdS/CFT, Phys. Rev. D 85 (2012) 104035 [arXiv:1108.5732] [INSPIRE].
D. Anninos, T. Hartman and A. Strominger, Higher spin realization of the dS/CFT correspondence, Class. Quant. Grav. 34 (2017) 015009 [arXiv:1108.5735] [INSPIRE].
X. Dong, B. Horn, E. Silverstein and G. Torroba, Moduli stabilization and the holographic RG for AdS and dS, JHEP 06 (2013) 089 [arXiv:1209.5392] [INSPIRE].
X. Dong, E. Silverstein and G. Torroba, De Sitter holography and entanglement entropy, JHEP 07 (2018) 050 [arXiv:1804.08623] [INSPIRE].
M. Miyaji and T. Takayanagi, Surface/state correspondence as a generalized holography, PTEP 2015 (2015) 073B03 [arXiv:1503.03542] [INSPIRE].
Y. Nomura, P. Rath and N. Salzetta, Pulling the boundary into the bulk, Phys. Rev. D 98 (2018) 026010 [arXiv:1805.00523] [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
D. Harlow and D. Stanford, Operator dictionaries and wave functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
A.B. Zamolodchikov, Expectation value of composite field \( T\overline{T} \) in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE].
F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].
A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, \( T\overline{T} \) -deformed 2D quantum field theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Solving the simplest theory of quantum gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].
L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \) , JHEP 04 (2018) 010 [arXiv:1611.03470] [INSPIRE].
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS 2 holography and \( T\overline{T} \) , JHEP 09 (2017) 136 [arXiv:1706.06604] [INSPIRE].
J. Cardy, The \( T\overline{T} \) deformation of quantum field theory as random geometry, JHEP 10 (2018) 186 [arXiv:1801.06895] [INSPIRE].
W. Cottrell and A. Hashimoto, Comments on \( T\overline{T} \) double trace deformations and boundary conditions, Phys. Lett. B 789 (2019) 251 [arXiv:1801.09708] [INSPIRE].
P. Kraus, J. Liu and D. Marolf, Cutoff AdS 3 versus the \( T\overline{T} \) deformation, JHEP 07 (2018) 027 [arXiv:1801.02714] [INSPIRE].
W. Donnelly and V. Shyam, Entanglement entropy and \( T\overline{T} \) deformation, Phys. Rev. Lett. 121 (2018) 131602 [arXiv:1806.07444] [INSPIRE].
T. Hartman, J. Kruthoff, E. Shaghoulian and A. Tajdini, Holography at finite cutoff with a T 2 deformation, JHEP 03 (2019) 004 [arXiv:1807.11401] [INSPIRE].
M. Taylor, TT deformations in general dimensions, arXiv:1805.10287 [INSPIRE].
G. Bonelli, N. Doroud and M. Zhu, \( T\overline{T} \) -deformations in closed form, JHEP 06 (2018) 149 [arXiv:1804.10967] [INSPIRE].
O. Aharony and T. Vaknin, The T T ∗ deformation at large central charge, JHEP 05 (2018) 166 [arXiv:1803.00100] [INSPIRE].
O. Aharony et al., Modular invariance and uniqueness of \( T\overline{T} \) deformed CFT, JHEP 01 (2019) 086 [arXiv:1808.02492] [INSPIRE].
S. Datta and Y. Jiang, \( T\overline{T} \) deformed partition functions, JHEP 08 (2018) 106 [arXiv:1806.07426] [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, \( T\overline{T} \) and LST, JHEP 07 (2017) 122 [arXiv:1701.05576] [INSPIRE].
M. Guica, An integrable Lorentz-breaking deformation of two-dimensional CFTs, SciPost Phys. 5 (2018) 048 [arXiv:1710.08415] [INSPIRE].
M. Baggio, A. Sfondrini, G. Tartaglino-Mazzucchelli and H. Walsh, On \( T\overline{T} \) deformations and supersymmetry, arXiv:1811.00533 [INSPIRE].
C.-K. Chang, C. Ferko and S. Sethi, Supersymmetry and \( T\overline{T} \) Deformations, arXiv:1811.01895 [INSPIRE].
J.A. Damia and D. Freedman work in progress.
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
S. Dubovsky, V. Gorbenko and G. Hernández-Chifflet, \( T\overline{T} \) partition function from topological gravity, JHEP 09 (2018) 158 [arXiv:1805.07386] [INSPIRE].
S. Deser and R. Jackiw, Three-dimensional cosmological gravity: dynamics of constant curvature, Annals Phys. 153 (1984) 405 [INSPIRE].
R. Bousso, A. Maloney and A. Strominger, Conformal vacua and entropy in de Sitter space, Phys. Rev. D 65 (2002) 104039 [hep-th/0112218] [INSPIRE].
E.J. Martinec, Conformal field theory, geometry and entropy, hep-th/9809021 [INSPIRE].
D. Marolf and M. Rangamani, Causality and the AdS Dirichlet problem, JHEP 04 (2012) 035 [arXiv:1201.1233] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
Z. Komargodski, The constraints of conformal symmetry on RG flows, JHEP 07 (2012) 069 [arXiv:1112.4538] [INSPIRE].
L. Susskind and E. Witten, The holographic bound in Anti-de Sitter space, hep-th/9805114 [INSPIRE].
V. Balasubramanian, B.D. Chowdhury, B. Czech and J. de Boer, Entwinement and the emergence of spacetime, JHEP 01 (2015) 048 [arXiv:1406.5859] [INSPIRE].
V. Balasubramanian et al., Entwinement in discretely gauged theories, JHEP 12 (2016) 094 [arXiv:1609.03991] [INSPIRE].
V. Balasubramanian, B. Craps, T. De Jonckheere and G. Sárosi, Entanglement versus entwinement in symmetric product orbifolds, JHEP 01 (2019) 190 [arXiv:1806.02871] [INSPIRE].
M. Rangamani, Gravity and hydrodynamics: lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
H. Casini and M. Huerta, On the RG running of the entanglement entropy of a circle, Phys. Rev. D 85 (2012) 125016 [arXiv:1202.5650] [INSPIRE].
O. Aharony, M. Berkooz and E. Silverstein, Multiple trace operators and nonlocal string theories, JHEP 08 (2001) 006 [hep-th/0105309] [INSPIRE].
D. Brattan, J. Camps, R. Loganayagam and M. Rangamani, CFT dual of the AdS Dirichlet problem: fluid/gravity on cut-off surfaces, JHEP 12 (2011) 090 [arXiv:1106.2577] [INSPIRE].
D. Anninos and D.M. Hofman, Infrared realization of dS 2 in AdS 2, Class. Quant. Grav. 35 (2018) 085003 [arXiv:1703.04622] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1811.07965
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Gorbenko, V., Silverstein, E. & Torroba, G. dS/dS and \( T\overline{T} \). J. High Energ. Phys. 2019, 85 (2019). https://doi.org/10.1007/JHEP03(2019)085
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2019)085