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 non-perturbatively 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.
Cite
@article{arxiv.1504.05991,
title = {Exact Path Integral for 3D Quantum Gravity},
author = {Norihiro Iizuka and Akinori Tanaka and Seiji Terashima},
journal= {arXiv preprint arXiv:1504.05991},
year = {2015}
}
Comments
5 pages. v2: boundary fermion argument added. v3: shorter version for Physical Review Letters