Holographic Dual of Crosscap Conformal Field Theory

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.