Abstract
We start from (3 + 1)-dimensional Einstein gravity with minimally coupled massless scalar matter, through spherical dimensional reduction, the matter theory is non-minimally coupled with the dilaton in (1 + 1)-dimensions. Despite its simplicity, constructing a self-consistent one-loop effective theory for this model remains a challenge, partially due to a Weyl-invariant ambiguity in the effective action. With a universal splitting property for the one-loop action, the ambiguity can be identified with the state-dependent part of the covariant quantum stress tensor. By introducing on-shell equivalent auxiliary fields to construct minimal candidates of Weyl-invariant terms, we derive a one-parameter family of one-loop actions with unique, regular, and physical stress tensors corresponding to the Boulware, Hartle-Hawking and Unruh states. We further study the back-reacted geometry and the corresponding quantum extremal islands that were inaccessible without a consistent one-loop theory. Along the way, we elaborate on the implications of our construction for the non-minimal dilaton gravity model.
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Acknowledgments
We thank Xi Dong, Steven Giddings, and Donald Marolf for their useful comments and encouragement of this work, and special thanks to Gary Horowitz for valuable feedback on the draft. We also thank Amirhossein Tajdini, Sean McBride, Diandian Wang, Ziyue Wang, and Wayne Weng for helpful discussions. C-H.W. was supported in part by the U.S. Department of Energy under Grant No. DE-SC0023275, and the Ministry of Education, Taiwan. J.X. was on the MURI grant and was supported in part by the U.S. Department of Energy under Grant No. DE-SC0023275. This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-19-1-0360.
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Wu, CH., Xu, J. Islands in non-minimal dilaton gravity: exploring effective theories for black hole evaporation. J. High Energ. Phys. 2023, 94 (2023). https://doi.org/10.1007/JHEP10(2023)094
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DOI: https://doi.org/10.1007/JHEP10(2023)094