Abstract
We study the gravitational edge mode of the Jackiw-Teitelboim (JT) gravity and its sl(2, ℝ) BF theory description with the asymptotic AdS2 boundary condition. We revisit the derivation of the Schwarzian theory from the wiggling boundary as an action for the gravitational edge mode. We present an alternative description for the gravitational edge mode from the metric fluctuation with the fixed boundary, which is often referred as “would-be gauge mode”. We clarify the relation between the wiggling boundary and the would-be gauge mode. We demonstrate a natural top-down derivation of PSL(2, ℝ) gauging and the path integral measure of the Schwarzian theory. In the sl(2, ℝ) BF theory, we incorporate the gravitational edge mode and derive the Schwarzian theory with PSL(2, ℝ) gauging. We also discuss the path integral measure from the Haar measure in the Iwasawa decomposition of PSL(2, ℝ).
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Acknowledgments
We would like to thank Ioannis Papadimitriou, Piljin Yi, Akhil Sivakumar and Frank Ferrari for discussions. P.N. and J.Y. would like to thank International Centre for Theoretical Sciences (ICTS), Tata institute of fundamental research, Bengaluru for hospitality and support during the initial stage of this work. The work of E.J. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1F1A1074977). The work of J.Y. was supported by the NRF grant funded by the Korea government (MSIT) (No. 2022R1A2C1003182). J.Y. is supported by an appointment to the JRG Program at the APCTP through the Science and Technology Promotion Fund and Lottery Fund of the Korean Government. J.Y. is also supported by the Korean Local Governments - Gyeongsangbuk-do Province and Pohang City. P.N would like to acknowledge SERB grant MTR/2021/00014.
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Joung, E., Narayan, P. & Yoon, J. Gravitational edge mode in asymptotically AdS2: JT gravity revisited. J. High Energ. Phys. 2024, 244 (2024). https://doi.org/10.1007/JHEP05(2024)244
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DOI: https://doi.org/10.1007/JHEP05(2024)244