Complex saddles of Chern-Simons gravity and dS3/CFT2 correspondence

It would be useful to deal with complex geometry when examining quantum gravity as in the case of no-boundary proposal by Hartle and Hawking. However, there would be too many saddles for complexified gravity, and it is necessary to determine which are allowable geometries in the sense of Witten. As a simple example, we examine three-dimensional gravity theory with positive cosmological constant described by Chern-Simons gauge theory.
In this talk, we first propose a dS/CFT correspondence involving the Chern-Simons gravity and provide strong evidence for it. Applying the holography, we then determine the set of allowable complex saddles for the Chern-Simons gravity from its dual conformal field theory.