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<p>We propose a holographic dual for 2D CFT defined on closed non-orientable manifolds, such as the real projective plane ℝℙ<sup>2</sup> and the Klein bottle 𝕂<sup>2</sup>. 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<sub>3</sub> spacetime with dS<sub>2</sub> end-of-the-world branes. In particular, the Lorentzian spacetime with a global dS<sub>2</sub> 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 ℝℙ<sup>2</sup> partition function (or the <i>p</i>-function), one-point function, and 𝕂<sup>2</sup> partition function, and see that they successfully reproduce the XCFT results. We also show a holographic <i>p</i>-theorem as an application.</p>

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Holographic dual of crosscap conformal field theory

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  • 发表日期：

    2025年3月12日

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  • Zixia Wei

摘要

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.