Cutoff brane vs the Karch-Randall brane: the fluctuating case
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917638693715968 |
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| author | Lin, Jiong Lu, Yizhou Wen, Qiang |
| author_facet | Lin, Jiong Lu, Yizhou Wen, Qiang |
| contents | Recently, certain holographic Weyl transformed CFT$_2$ is proposed to capture the main features of the AdS$_3$/BCFT$_2$ correspondence \cite{Basu:2022crn,Basu:2023wmv}. In this paper, by adapting the Weyl transformation, we simulate a generalized AdS/BCFT set-up where the fluctuation of the Karch-Randall (KR) brane is considered. In the gravity dual of the Weyl transformed CFT, the so-called cutoff brane induced by the Weyl transformation plays the same role as the KR brane. Unlike the non-fluctuating configuration, in the $2d$ effective theory the additional twist operator is inserted at a different place, compared with the one inserted on the brane. Though this is well-understood in the Weyl transformed CFT set-up, it is confusing in the AdS/BCFT set-up where the effective theory is supposed to locate on the brane. This confusion indicates that the KR brane may be emergent from the boundary CFT$_2$ via the Weyl transformations.
We also calculate the balanced partial entanglement (BPE) in the fluctuating brane configurations and find it coincide with the entanglement wedge cross-section (EWCS). This is a non-trivial test for the correspondence between the BPE and the EWCS, and a non-trivial consistency check for the Weyl transformed CFT set-up. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_03531 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cutoff brane vs the Karch-Randall brane: the fluctuating case Lin, Jiong Lu, Yizhou Wen, Qiang High Energy Physics - Theory General Relativity and Quantum Cosmology Quantum Physics Recently, certain holographic Weyl transformed CFT$_2$ is proposed to capture the main features of the AdS$_3$/BCFT$_2$ correspondence \cite{Basu:2022crn,Basu:2023wmv}. In this paper, by adapting the Weyl transformation, we simulate a generalized AdS/BCFT set-up where the fluctuation of the Karch-Randall (KR) brane is considered. In the gravity dual of the Weyl transformed CFT, the so-called cutoff brane induced by the Weyl transformation plays the same role as the KR brane. Unlike the non-fluctuating configuration, in the $2d$ effective theory the additional twist operator is inserted at a different place, compared with the one inserted on the brane. Though this is well-understood in the Weyl transformed CFT set-up, it is confusing in the AdS/BCFT set-up where the effective theory is supposed to locate on the brane. This confusion indicates that the KR brane may be emergent from the boundary CFT$_2$ via the Weyl transformations. We also calculate the balanced partial entanglement (BPE) in the fluctuating brane configurations and find it coincide with the entanglement wedge cross-section (EWCS). This is a non-trivial test for the correspondence between the BPE and the EWCS, and a non-trivial consistency check for the Weyl transformed CFT set-up. |
| title | Cutoff brane vs the Karch-Randall brane: the fluctuating case |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2312.03531 |