Superpotential of the M-theory conifold and type IIA string theory

TL;DR

This paper explores the superpotential in M-theory on a G2 manifold and its relation to type IIA string theory, revealing connections involving dilogarithms, Heisenberg groups, and instanton effects across different theories.

Contribution

It establishes a detailed comparison between membrane instanton superpotentials in M-theory and hypermultiplet moduli space structures in type IIA string theory, highlighting new mathematical connections.

Findings

Superpotential expressed via dilogarithm with Heisenberg monodromy.

Comparison of M-theory superpotential to type IIA hypermultiplet moduli space.

Identification of dilogarithm and Heisenberg group roles in different string theory contexts.

Abstract

The membrane instanton superpotential for $M$-theory on the $G_2$ holonomy manifold given by the cone on ${\bf S^3}\x {\bf S^3}$ is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dilogarithm for the deformed conifold and to a flat bundle related to a conifold period, the Heisenberg group and the dilogarithm appearing in five-dimensional Seiberg/Witten theory.