An eight-dimensional approach to G_2 manifolds

TL;DR

This paper presents a systematic method for constructing G_2 holonomy manifolds with specific symmetries using eight-dimensional supergravity, generalizing known metrics and introducing new scalar field interactions.

Contribution

It develops a general framework for G_2 manifolds with SU(2)xSU(2) symmetry, extending the Bryant-Salamon metric and incorporating scalar fields into the twist mechanism.

Findings

Derived a general first order differential system for the metric functions.

Identified that only six of nine metric functions are independent.

Generalized the twist relating spin and gauge connections with scalar fields.

Abstract

We develop a systematic approach to G_2 holonomy manifolds with an SU(2)xSU(2) isometry using maximal eight-dimensional gauged supergravity to describe D6-branes wrapped on deformed three-spheres. A quite general metric ansatz that generalizes the celebrated Bryant-Salamon metric involves nine functions. We show that only six of them are the independent ones and derive the general first order system of differential equations that they obey. As a byproduct of our analysis, we generalize the notion of the twist that relates the spin and gauge connections in a way that involves non-trivially the scalar fields.