The Virasoro TQFT approach to 3D gravity and the sum over topologies (QuIG Seminar)

In the first part of this talk, I will review the construction of Virasoro TQFT from the Chern–Simons formulation of pure AdS_3 gravity and its application to the statistics of two-dimensional holographic CFT data. I will then discuss its extension to three-dimensional de Sitter gravity and its relation to the double-scaled SYK model. In the second part, I will address the issue of topological invariance in Virasoro TQFT. Despite being “topological,” its partition function is not well-defined on arbitrary three-manifolds, distinguishing it from conventional
Reshetikhin–Turaev–Witten TQFTs. I will explain how far the standard proofs of topological invariance can be generalized to this framework.
Finally, I will comment on the role of the sum over topologies in the 3D gravitational path integral.