Abstract
We study the random geometry approach to the \( T\overline{T} \) deformation of 2d conformal field theory developed by Cardy and discuss its realization in a gravity dual. In this representation, the gravity dual of the \( T\overline{T} \) deformation becomes a straightforward translation of the field theory language. Namely, the dual geometry is an ensemble of AdS3 spaces or BTZ black holes, without a finite cutoff, but instead with randomly fluctuating boundary diffeomorphisms. This reflects an increase in degrees of freedom in the renormalization group flow to the UV by the irrelevant \( T\overline{T} \) operator. We streamline the method of computation and calculate the energy spectrum and the thermal free energy in a manner that can be directly translated into the gravity dual language. We further generalize this approach to correlation functions and reproduce the all-order result with universal logarithmic corrections computed by Cardy in a different method. In contrast to earlier proposals, this version of the gravity dual of the \( T\overline{T} \) deformation works not only for the energy spectrum and the thermal free energy but also for correlation functions.
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References
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].
S. Weinberg, Critical Phenomena for Field Theorists, in The Subnuclear Series. Vol 14: Understanding the Fundamental Constituents of Matter, Springer, Berlin Germany (1978), pg. 1,
S. Weinberg, Ultraviolet Divergences In Quantum Theories Of Gravitation, in General Relativity: an Einstein centenary survey, Cambridge University Press, Cambridge U.K. (1980), pg. 790.
S. Dubovsky, R. Flauger and V. Gorbenko, Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS2 holography and \( T\overline{T} \), JHEP 09 (2017) 136 [arXiv:1706.06604] [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].
J. Haruna, T. Ishii, H. Kawai, K. Sakai and K. Yoshida, Large N analysis of \( T\overline{T} \)-deformation and unavoidable negative-norm states, JHEP 04 (2020) 127 [arXiv:2002.01414] [INSPIRE].
J. Cardy, The \( T\overline{T} \) deformation of quantum field theory as random geometry, JHEP 10 (2018) 186 [arXiv:1801.06895] [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].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
J. Cardy, \( T\overline{T} \) deformation of correlation functions, JHEP 19 (2020) 160 [arXiv:1907.03394] [INSPIRE].
P. Kraus, J. Liu and D. Marolf, Cutoff AdS3 versus the \( T\overline{T} \) deformation, JHEP 07 (2018) 027 [arXiv:1801.02714] [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].
M. Guica and R. Monten, \( T\overline{T} \) and the mirage of a bulk cutoff, arXiv:1906.11251 [INSPIRE].
S.S. Gubser, A. Hashimoto, I.R. Klebanov and M. Krasnitz, Scalar absorption and the breaking of the world volume conformal invariance, Nucl. Phys. B 526 (1998) 393 [hep-th/9803023] [INSPIRE].
K.A. Intriligator, Maximally supersymmetric RG flows and AdS duality, Nucl. Phys. B 580 (2000) 99 [hep-th/9909082] [INSPIRE].
M. Caselle, D. Fioravanti, F. Gliozzi and R. Tateo, Quantisation of the effective string with TBA, JHEP 07 (2013) 071 [arXiv:1305.1278] [INSPIRE].
N. Callebaut, J. Kruthoff and H. Verlinde, \( T\overline{T} \) deformed CFT as a non-critical string, JHEP 04 (2020) 084 [arXiv:1910.13578] [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, \( \mathrm{T}\overline{\mathrm{T}} \) and LST, JHEP 07 (2017) 122 [arXiv:1701.05576] [INSPIRE].
G. Giribet, \( T\overline{T} \)-deformations, AdS/CFT and correlation functions, JHEP 02 (2018) 114 [arXiv:1711.02716] [INSPIRE].
J.P. Babaro, V.F. Foit, G. Giribet and M. Leoni, \( T\overline{T} \) type deformation in the presence of a boundary, JHEP 08 (2018) 096 [arXiv:1806.10713] [INSPIRE].
G. Giribet and M. Leoni, Current-current deformations, conformal integrals and correlation functions, JHEP 04 (2020) 194 [arXiv:2003.02864] [INSPIRE].
J. Cardy, Quantum Quenches to a Critical Point in One Dimension: some further results, J. Stat. Mech. 1602 (2016) 023103 [arXiv:1507.07266] [INSPIRE].
L. Freidel, Reconstructing AdS/CFT, arXiv:0804.0632 [INSPIRE].
H.L. Verlinde, Conformal Field Theory, 2-D Quantum Gravity and Quantization of Teichmüller Space, Nucl. Phys. B 337 (1990) 652 [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].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
J. Brown, J. Creighton and R.B. Mann, Temperature, energy and heat capacity of asymptotically anti-de Sitter black holes, Phys. Rev. D 50 (1994) 6394 [gr-qc/9405007] [INSPIRE].
J. Brown and J.W. York, Jr., Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [INSPIRE].
I. Heemskerk and J. Polchinski, Holographic and Wilsonian Renormalization Groups, JHEP 06 (2011) 031 [arXiv:1010.1264] [INSPIRE].
O. Aharony and T. Vaknin, The TT* deformation at large central charge, JHEP 05 (2018) 166 [arXiv:1803.00100] [INSPIRE].
K. Yonekura, On the Trace Anomaly and the Anomaly Puzzle in N = 1 Pure Yang-Mills, JHEP 03 (2012) 029 [arXiv:1202.1514] [INSPIRE].
K. Fujikawa, Energy Momentum Tensor in Quantum Field Theory, Phys. Rev. D 23 (1981) 2262 [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
W. Donnelly and V. Shyam, Entanglement entropy and \( T\overline{T} \) deformation, Phys. Rev. Lett. 121 (2018) 131602 [arXiv:1806.07444] [INSPIRE].
B. Chen, L. Chen and P.-X. Hao, Entanglement entropy in \( T\overline{T} \)-deformed CFT, Phys. Rev. D 98 (2018) 086025 [arXiv:1807.08293] [INSPIRE].
A. Banerjee, A. Bhattacharyya and S. Chakraborty, Entanglement Entropy for TT deformed CFT in general dimensions, Nucl. Phys. B 948 (2019) 114775 [arXiv:1904.00716] [INSPIRE].
P. Caputa, S. Datta and V. Shyam, Sphere partition functions \& cut-off AdS, JHEP 05 (2019) 112 [arXiv:1902.10893] [INSPIRE].
G. Jafari, A. Naseh and H. Zolfi, Path Integral Optimization for \( T\overline{T} \) Deformation, Phys. Rev. D 101 (2020) 026007 [arXiv:1909.02357] [INSPIRE].
M. Taylor, TT deformations in general dimensions, arXiv:1805.10287 [INSPIRE].
T. Hartman, J. Kruthoff, E. Shaghoulian and A. Tajdini, Holography at finite cutoff with a T2 deformation, JHEP 03 (2019) 004 [arXiv:1807.11401] [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
A. Strominger, Inflation and the dS/CFT correspondence, JHEP 11 (2001) 049 [hep-th/0110087] [INSPIRE].
S.S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [INSPIRE].
C.P. Herzog, A. Karch, P. Kovtun, C. Kozcaz and L.G. Yaffe, Energy loss of a heavy quark moving through N = 4 supersymmetric Yang-Mills plasma, JHEP 07 (2006) 013 [hep-th/0605158] [INSPIRE].
I. Bena and A. Tyukov, BTZ Trailing Strings, JHEP 04 (2020) 046 [arXiv:1911.12821] [INSPIRE].
I. Bena, S. El-Showk and B. Vercnocke, Black Holes in String Theory, Springer Proc. Phys. 144 (2013) 59.
J.R. David, G. Mandal and S.R. Wadia, Microscopic formulation of black holes in string theory, Phys. Rept. 369 (2002) 549 [hep-th/0203048] [INSPIRE].
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. 430 (1994) 485] [hep-th/9407087] [INSPIRE].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
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Hirano, S., Shigemori, M. Random boundary geometry and gravity dual of \( T\overline{T} \) deformation. J. High Energ. Phys. 2020, 108 (2020). https://doi.org/10.1007/JHEP11(2020)108
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DOI: https://doi.org/10.1007/JHEP11(2020)108