G2 Hitchin functionals at one loop

TL;DR

This paper computes the one-loop partition function of topological M-theory using Hitchin functionals, explores its relation to generalized G2 geometry and topological G2 string, and analyzes background dependence.

Contribution

It provides the first explicit one-loop partition function calculation for topological M-theory based on Hitchin functionals and connects it to generalized G2 geometry and topological string theory.

Findings

Calculated the one-loop partition function for topological M-theory.

Established a relation between extended G2 geometry and the Hitchin functional.

Analyzed the background dependence of the partition functions.

Abstract

We consider the quantization of the effective target space description of topological M-theory in terms of the Hitchin functional whose critical points describe seven-manifolds with G2 structure. The one-loop partition function for this theory is calculated and an extended version of it, that is related to generalized G2 geometry, is compared with the topological G2 string. We relate the reduction of the effective action for the extended G2 theory to the Hitchin functional description of the topological string in six dimensions. The dependence of the partition functions on the choice of background G2 metric is also determined.