Three-Dimensional Gravity on Spaces with Multiple Boundaries

Three-dimensional gravity on spaces with multiple boundaries is classically solved by using the Chern-Simons formulation. The gauge-invariant classical phase space is explicitly constructed. The Hilbert space is shown not to tensor-factorize into the product of two Hilbert spaces, one for each boundary, due to zero mode degrees of freedom (holonomies) that are shared by the two boundary theories. Based on JHEP 03 (2020) 064.