Communications in Number Theory and Physics
Volume 2 (2008)
Partition functions of three-dimensional pure gravity
Pages: 285 – 324
The three-dimensional pure quantum gravity with a negativecosmological constant has been conjectured to be dual to anextremal conformal field theory (ECFT), of central charge$c=24k$ for some positive integer $k$. We compute the partitionfunction of the dual ECFT by summing over gravitationalinstanton contributions. In particular, we conjecture an exactexpression for the contribution from handlebodies to thepartition function for all genera and all values of $k$ andprovide non-trivial evidences for the conjecture at genus two.