Abstract
We show that 3-dimensional AdS spacetime can be semiclassically unstable due to strongly interacting quantum field effects. In our previous paper, we have pointed out the possibility of such an instability of AdS3 by inspecting linear perturbations of the (covering space of) static BTZ black hole with AdS4 gravity dual in the context of holographic semiclassical problems. In the present paper, we further study this issue from thermodynamic viewpoint by constructing asymptotically AdS3 semiclassical solutions and computing free energies of the solutions. We find two asymptotically AdS3 solutions to the semiclassical Einstein equations with non-vanishing source term: the one whose free energy is smaller than that of the BTZ with vanishing source term and the other whose free energy is smaller than that of the global AdS3 with no horizon (thus manifestly zero-temperature background). The instability found in this paper implies the breakdown of the maximal symmetries of AdS3, and its origin is different from the well-known semiclassical linear instability since our holographic semiclassical Einstein equations in 3-dimensions do not involve higher order derivative terms.
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References
G.T. Horowitz and R.M. Wald, Dynamics of Einstein’s Equation Modified by a Higher Order Derivative Term, Phys. Rev. D 17 (1978) 414 [INSPIRE].
G.T. Horowitz, Semiclassical relativity: the weak field limit, Phys. Rev. D 21 (1980) 1445 [INSPIRE].
W.M. Suen, Minkowski Space-time Is Unstable in Semiclassical Gravity, Phys. Rev. Lett. 62 (1989) 2217 [INSPIRE].
A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
A. Vilenkin, Classical and Quantum Cosmology of the Starobinsky Inflationary Model, Phys. Rev. D 32 (1985) 2511 [INSPIRE].
G. Compere and D. Marolf, Setting the boundary free in AdS/CFT, Class. Quant. Grav. 25 (2008) 195014 [arXiv:0805.1902] [INSPIRE].
A. Ishibashi, K. Maeda and T. Okamura, Semiclassical Einstein equations from holography and boundary dynamics, JHEP 05 (2023) 212 [arXiv:2301.12170] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [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].
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].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
J.Z. Simon, The Stability of flat space, semiclassical gravity, and higher derivatives, Phys. Rev. D 43 (1991) 3308 [INSPIRE].
J.Z. Simon, No Starobinsky inflation from selfconsistent semiclassical gravity, Phys. Rev. D 45 (1992) 1953 [INSPIRE].
R. Emparan, A.M. Frassino and B. Way, Quantum BTZ black hole, JHEP 11 (2020) 137 [arXiv:2007.15999] [INSPIRE].
Acknowledgments
We wish to thank Roberto Emparan for useful discussions. We are grateful to the long term workshop YITP-T-23-01 held at YITP, Kyoto University, where a part of this work was done. This work is supported in part by JSPS KAKENHI Grant No. 15K05092, 20K03938 (A.I.), 20K03975 (K.M.), 17K05427(T.O.), and also supported by MEXT KAKENHI Grant-in-Aid for Transformative Research Areas A Extreme Universe No.21H05186 (A.I. and K.M.) and 21H05182.
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ArXiv ePrint: 2312.10311
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Ishibashi, A., Maeda, K. & Okamura, T. Symmetry breaking of 3-dimensional AdS in holographic semiclassical gravity. J. High Energ. Phys. 2024, 146 (2024). https://doi.org/10.1007/JHEP02(2024)146
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DOI: https://doi.org/10.1007/JHEP02(2024)146