Y. Jiang: ensor network and Hartle-Hawking state in 3d gravity (Northeastern)

I will explain the triangulation for the path-integral of Liouville CFT on any 2d surfaces, by proposing a boundary condition for this CFT that allows small holes to close. This will produce an exact analytical tensor network that admits an interpretation of a state-sum of a 3D topological theory constructed with quantum 6j symbols of U_q(Sl(2,R)) with non-trivial boundary conditions, and reduces to Einstein-Hilbert gravity evaluated on hyperbolic spaces in the large central charge limit. The triangulation coincides with producing a network of geodesics in the AdS bulk, which can be changed making use of the pentagon identity and orthogonality condition satisfied by the 6j symbols, and arranged into a precise holographic tensor network. If time permits, I will also describe an identification for the Hartle-Hawking state of BTZ black holes as Liouville ZZ boundary states.