Holographic dual of crosscap conformal field theory

Abstract

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.

Keywords

• AdS-CFT Correspondence
• de Sitter space