Holographic dual of crosscap conformal field theory
Abstract We propose a holographic dual for 2D CFT defined on closed non-orientable manifolds, such as the real projective plane ℝℙ2 and the Klein bottle 𝕂2. Such CFT can be constructed by introducing antipodally identified cuttings, i.e. crosscaps, to a sphere and hence called crosscap CFT (XCFT). T...
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2025)086 |
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| Summary: | Abstract We propose a holographic dual for 2D CFT defined on closed non-orientable manifolds, such as the real projective plane ℝℙ2 and the Klein bottle 𝕂2. 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 AdS3 spacetime with dS2 end-of-the-world branes. In particular, the Lorentzian spacetime with a global dS2 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 ℝℙ2 partition function (or the p-function), one-point function, and 𝕂2 partition function, and see that they successfully reproduce the XCFT results. We also show a holographic p-theorem as an application. |
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| ISSN: | 1029-8479 |