Non-Perturbative 3D Quantum Gravity: Quantum Boundary States and Exact Partition Function

Understand

We push forward the investigation of holographic dualities in 3D quantum gravity formulated as a topological quantum field theory, studying the correspondence between boundary and bulk structures.

• Working with the Ponzano-Regge topological state-sum model defining an exact discretization of 3d quantum gravity, we analyze how the partition function for a solid twisted torus depends on the boundary quantum state.
• This configuration is relevant to the AdS${}_{3}$/CFT${}_{2}$ correspondence.
• We introduce boundary spin network states with coherent superposition of spins on a square lattice on the boundary surface.