Let's Twist Again: General Metrics of G(2) Holonomy from Gauged Supergravity

TL;DR

This paper constructs all complete cohomogeneity one G(2) holonomy metrics with S^3 x S^3 principal orbits using gauged supergravity, generalizing the twisting procedure and revealing new geometric structures.

Contribution

It introduces a novel method to generate G(2) holonomy metrics from gauged supergravity, extending the twisting technique to a broader class of solutions.

Findings

Realization of Hitchin system in eight-dimensional supergravity

Implementation of flop transformations in the supergravity framework

Complete classification of cohomogeneity one G(2) metrics with specified orbits

Abstract

We construct all complete metrics of cohomogeneity one G(2) holonomy with S^3 x S^3 principal orbits from gauged supergravity. Our approach rests on a generalization of the twisting procedure used in this framework. It corresponds to a non-trivial embedding of the special Lagrangian three-cycle wrapped by the D6-branes in the lower dimensional supergravity. There are constraints that neatly reduce the general ansatz to a six functions one. Within this approach, the Hitchin system and the flop transformation are nicely realized in eight dimensional gauged supergravity.