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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2402.15836 |
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| _version_ | 1866910499275276288 |
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| author | Chandra, Ashish Li, Zhengjiang Wen, Qiang |
| author_facet | Chandra, Ashish Li, Zhengjiang Wen, Qiang |
| contents | Recently it was proposed that, the AdS/BCFT correspondence can be simulated by a holographic Weyl transformed CFT$_2$, where the cut-off brane plays the role of the Karch-Randall (KR) brane \cite{Basu:2022crn}. In this paper, we focus on the Weyl transformation that optimizes the path integral computation of the reduced density matrix for a single interval in a holographic CFT$_2$. When we take the limit that one of the endpoint of the interval goes to infinity (a half line), such a holographic Weyl transformed CFT$_2$ matches the AdS/BCFT configuration for a BCFT with one boundary. Without taking the limit, the induced cutoff brane becomes a circle passing through the two endpoints of the interval. We assume that the cutoff brane also plays the same role as the KR brane in AdS/BCFT, hence the path-integral-optimized purification for the interval is in the island phase. This explains the appearance of negative mutual information observed in \cite{Camargo:2022mme}. We check that, the entanglement entropy and the balanced partial entanglement entropy (BPE) calculated via the island formulas, exactly match with the RT formula and the entanglement wedge cross-section (EWCS), which are allowed to anchor on the cutoff brane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15836 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement islands and cutoff branes from path-integral optimization Chandra, Ashish Li, Zhengjiang Wen, Qiang High Energy Physics - Theory Recently it was proposed that, the AdS/BCFT correspondence can be simulated by a holographic Weyl transformed CFT$_2$, where the cut-off brane plays the role of the Karch-Randall (KR) brane \cite{Basu:2022crn}. In this paper, we focus on the Weyl transformation that optimizes the path integral computation of the reduced density matrix for a single interval in a holographic CFT$_2$. When we take the limit that one of the endpoint of the interval goes to infinity (a half line), such a holographic Weyl transformed CFT$_2$ matches the AdS/BCFT configuration for a BCFT with one boundary. Without taking the limit, the induced cutoff brane becomes a circle passing through the two endpoints of the interval. We assume that the cutoff brane also plays the same role as the KR brane in AdS/BCFT, hence the path-integral-optimized purification for the interval is in the island phase. This explains the appearance of negative mutual information observed in \cite{Camargo:2022mme}. We check that, the entanglement entropy and the balanced partial entanglement entropy (BPE) calculated via the island formulas, exactly match with the RT formula and the entanglement wedge cross-section (EWCS), which are allowed to anchor on the cutoff brane. |
| title | Entanglement islands and cutoff branes from path-integral optimization |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2402.15836 |