M-theory compactifications on certain `toric' cones of $G_2$ holonomy

TL;DR

This paper develops methods to analyze singularities in G2 cones related to toric hyperkahler spaces, enabling the determination of gauge groups in M-theory compactifications and exploring their T-dual IIA/IIB descriptions.

Contribution

It introduces new techniques for studying G2 cone singularities and their implications for M-theory compactifications, including criteria for good isometries and T-dual descriptions.

Findings

Determined low energy gauge groups for a large family of G2 compactifications.

Identified conditions for isometries leading to weakly-coupled IIA models.

Constructed explicit examples of backgrounds with desirable properties.

Abstract

We develop methods to study the singularities of certain $G_2$ cones related to toric hyperkahler spaces and Einstein selfdual orbifolds. This allows us to determine the low energy gauge groups of chiral N=1 compactifications of M-theory on a large family of such backgrounds, which includes the models recently studied by Acharya and Witten. All M-theory compactifications belonging to our family admit a $T^2$ of isometries, and therefore T-dual IIA and IIB descriptions. We argue that reduction through such an isometry leads generically to systems of weakly and strongly coupled IIA 6-branes, T-dual to delocalized type IIB 5-branes. We find a simple criterion for the existence of a `good' isometry which leads to IIA models containing only weakly-coupled D6-branes, and construct examples of such backgrounds. Some of the methods we develop may also apply to different situations, such as the study of certain singularities in the hypermultiplet moduli space of N=2 supergravity in four dimensions.