Partition Functions of Three Dimensional Gravity

          @misc{ pirsa_PIRSA:07110061,
            doi = {10.48660/07110061},
            url = {https://pirsa.org/07110061},
            author = {Maloney, Alexander},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Partition Functions of Three Dimensional Gravity},
            publisher = {Perimeter Institute},
            year = {2007},
            month = {nov},
            note = {PIRSA:07110061 see, \url{https://pirsa.org}}
          }
          

Abstract

We consider pure three dimensional quantum gravity with a negative cosmological constant. The torus partition function can be computed exactly as a sum over geometries, including all known quantum corrections. The answer provides important clues about the structure of quantum gravity; in particular, in order for the theory to be a proper quantum mechanical system some extra ingredients are needed beyond the usual real geometries considered in general relativity. One possiblity is that complex geometries need to be included; this leads to holomorphically factorized partition functions. These partition functions provide a wealth of information about black hole microphysics. For example, the Hawking-page phase transition can be studied exactly; it is a phase transition of the type described by Lee and Yang, which is associated with a condensation of zeros in the complex temperature plane.