Gravitational Edge Mode in Asymptotically AdS$_2$: JT Gravity Revisited
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| Format: | Preprint |
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2023
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| author | Joung, Euihun Narayan, Prithvi Yoon, Junggi |
| author_facet | Joung, Euihun Narayan, Prithvi Yoon, Junggi |
| contents | We study the gravitational edge mode of the Jackiw-Teitelboim (JT) gravity and its $sl(2,\mathbb{R})$ BF theory description with the asymptotic AdS$_2$ 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 $PSL(2,\mathbb{R})$ gauging and the path integral measure of the Schwarzian theory. In the $sl(2,\mathbb{R})$ BF theory, we incorporate the gravitational edge mode and derive the Schwarzian theory with $PSL(2,\mathbb{R})$ gauging. We also discuss the path integral measure from the Haar measure in the Iwasawa decomposition of $PSL(2,\mathbb{R})$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_06088 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gravitational Edge Mode in Asymptotically AdS$_2$: JT Gravity Revisited Joung, Euihun Narayan, Prithvi Yoon, Junggi High Energy Physics - Theory Strongly Correlated Electrons General Relativity and Quantum Cosmology We study the gravitational edge mode of the Jackiw-Teitelboim (JT) gravity and its $sl(2,\mathbb{R})$ BF theory description with the asymptotic AdS$_2$ 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 $PSL(2,\mathbb{R})$ gauging and the path integral measure of the Schwarzian theory. In the $sl(2,\mathbb{R})$ BF theory, we incorporate the gravitational edge mode and derive the Schwarzian theory with $PSL(2,\mathbb{R})$ gauging. We also discuss the path integral measure from the Haar measure in the Iwasawa decomposition of $PSL(2,\mathbb{R})$. |
| title | Gravitational Edge Mode in Asymptotically AdS$_2$: JT Gravity Revisited |
| topic | High Energy Physics - Theory Strongly Correlated Electrons General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2304.06088 |