In recent years, the correspondence between boundary conformal field theory (BCFT) and AdS3 gravity with AdS2 end-of-the-world (EOW) branes has played an important role in advancing our understanding of quantum aspects of AdS2 gravity, including the island formula. Conversely, while AdS3 gravity with dS2 EOW branes is expected to aid in understanding dS2 quantum gravity, its CFT dual has long remained unknown.
In this talk, I propose a correspondence between a 2D crosscap CFT (XCFT)—a CFT defined on 2D non-orientable manifolds, such as the real projective plane (RP2) and the Klein bottle (K2)—and AdS3 Einstein gravity with dS2 EOW branes. In this framework, the Z2 quotient of a global dS2 brane is described by the unitary time evolution of a crosscap state in the CFT, post-selected on the CFT ground state. After motivating the correspondence from a cobordism theory perspective, we verify that the holographic RP2 partition function (or p-function), the one-point function, and the Klein bottle partition function successfully reproduce the CFT results. As an application, we also demonstrate that the holographic p-function is monotonic under a holographic RG flow, although the corresponding CFT dual remains to be determined.
The dS2 geometry appearing in this setup is not a global dS but a non-orientable Z2 quotient, suggesting that it may be more fundamental than global dS in constructing dS holography. I will briefly discuss some classical and quantum aspects of these geometries.
This talk is based on 2405.03755 and ongoing work.