Appears in collection : Korea-France Joint Workshop on String Theory

Two of the central open problems in three-dimensional quantum gravity are how to sum over all 3d topologies, which is necessary for self-consistency, and how to define the dual ensemble, which is believed to include all CFTs at large central charge. In this talk I present a model of 3d gravity in which both of these questions can be addressed explicitly. The model, formulated within the framework of TQFT gravity, is built from n copies of the rational version of Virasoro TQFT at central charge $c = 1/2$, summed over all 3d topologies according to a universal, TQFT-independent prescription. The resulting 3d gravitational theory is dual to the ensemble of all 2d CFTs with central charge $c = n/2$ and chiral algebra $(Vir_{c=1/2})^n$, which can be verified by comparing the partition functions on both sides of the duality. I will explain how the sum over topologies is defined and performed, and describe the structure of the resulting partition function. I will then discuss the large central charge limit and close with the lessons for conventional 3d gravity.