title: Exact Path Integral for 3D Quantum Gravity.
abstract: Three-dimensional Euclidean pure gravity with a negative cosmological constant can be formulated in terms of the Chern-Simons theory, classically. This theory can be written in a supersymmetric way by introducing auxiliary gauginos and scalars. We calculate the exact partition function of this Chern-Simons theory by using the localization technique. Thus, we obtain the quantum gravity partition function, assuming that it can be obtained nonperturbatively by summing over partition functions of the Chern-Simons theory on topologically different manifolds. The resultant partition function is modular invariant, and, in the case in which the central charge is expected to be 24, it is the J function, predicted by Witten.
authors.affiliation: Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan.
authors.forename: Norihiro
authors.initials: N
authors.lastname: Iizuka
authors.affiliation: Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan.|Interdisciplinary Theoretical Science Research Group, RIKEN, Wako 351-0198, Japan.
authors.forename: Akinori
authors.initials: A
authors.lastname: Tanaka
authors.affiliation: Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan.
authors.forename: Seiji
authors.initials: S
authors.lastname: Terashima