Abstract
In this paper, we consider how to formulate semiclassical problems in the context of the AdS/CFT correspondence, based on the proposal of Compere and Marolf. Our prescription involves the effective action with self-action term for boundary dynamical fields, which can be viewed as imposing mixed boundary conditions for the gravity dual. We derive the semiclassical Einstein equations sourced by boundary CFT stress-energy tensor. Analyzing perturbations of the holographic semiclassical Einstein equations, we find a universal parameter γd which controls the contribution from boundary CFTs and specifies dynamics on the AdS boundary. As a simple example, we examine the semiclassical Einstein equations in 3-dimensions with 4-dimensional AdS gravity dual, and show that the boundary BTZ black hole with vanishing expectation value of the stress-energy tensor becomes unstable due to the backreaction from quantum stress-energy tensor when the parameter γd exceeds a certain critical value.
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Acknowledgments
This work was supported in part by JSPS KAKENHI Grant No. 15K05092, 20K03938, 20K03975, 17K05451 (A.I.), 20K03975 (K.M.), and 17K05427(T.O.), and also supported by MEXT KAKENHI Grant-in-Aid for Transformative Research Areas A Extreme Universe No. 21H05182, 21H05186 (A.I. and K.M.).
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Ishibashi, A., Maeda, K. & Okamura, T. Semiclassical Einstein equations from holography and boundary dynamics. J. High Energ. Phys. 2023, 212 (2023). https://doi.org/10.1007/JHEP05(2023)212
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DOI: https://doi.org/10.1007/JHEP05(2023)212