Holographic Dual of Crosscap Conformal Field Theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908322870853632 |
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| author | Wei, Zixia |
| author_facet | Wei, Zixia |
| contents | We propose a holographic dual for 2D CFT defined on closed non-orientable manifolds, such as the real projective plane $\mathbb{RP}^2$ and the Klein bottle $\mathbb{K}^2$. Such CFT can be constructed by introducing antipodally identified cuttings, i.e. crosscaps, to a sphere and hence called crosscap CFT (XCFT). The gravity dual is AdS$_3$ spacetime with dS$_2$ end-of-the-world branes. In particular, the Lorentzian spacetime with a global dS$_2$ brane is dual to the unitary time evolution of a crosscap state in CFT, post-selected on the CFT ground state. We compute the holographic $\mathbb{RP}^2$ partition function (or the $p$-function), one-point function, and $\mathbb{K}^2$ partition function, and see that they successfully reproduce the XCFT results. We also show a holographic $p$-theorem as an application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03755 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holographic Dual of Crosscap Conformal Field Theory Wei, Zixia High Energy Physics - Theory We propose a holographic dual for 2D CFT defined on closed non-orientable manifolds, such as the real projective plane $\mathbb{RP}^2$ and the Klein bottle $\mathbb{K}^2$. Such CFT can be constructed by introducing antipodally identified cuttings, i.e. crosscaps, to a sphere and hence called crosscap CFT (XCFT). The gravity dual is AdS$_3$ spacetime with dS$_2$ end-of-the-world branes. In particular, the Lorentzian spacetime with a global dS$_2$ brane is dual to the unitary time evolution of a crosscap state in CFT, post-selected on the CFT ground state. We compute the holographic $\mathbb{RP}^2$ partition function (or the $p$-function), one-point function, and $\mathbb{K}^2$ partition function, and see that they successfully reproduce the XCFT results. We also show a holographic $p$-theorem as an application. |
| title | Holographic Dual of Crosscap Conformal Field Theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.03755 |