Singular 7-manifolds with G_2 holonomy and intersecting 6-branes

TL;DR

This paper constructs G_2 holonomy 7-manifolds as bundles over singular quaternionic spaces, explores their isometries, and discusses their M-theory compactifications leading to intersecting 6-branes, with potential singularity resolution via membrane instantons.

Contribution

It introduces a new class of G_2 manifolds based on singular quaternionic bases with tunable parameters, linking geometric structures to intersecting brane configurations in M-theory.

Findings

Constructed G_2 manifolds as R^3 bundles over singular quaternionic spaces.

Analyzed isometries and fixed points of the constructed manifolds.

Proposed membrane instantons as a mechanism to resolve curvature singularities.

Abstract

A 7-manifold with G_2 holonomy can be constructed as a R^3 bundle over a quaternionic space. We consider a quaternionic base space which is singular and its metric depends on three parameters, where one of them corresponds to an interpolation between S^4 and CP^2 or its non-compact analogs. This 4-d Einstein space has four isometries and the fixed point set of a generic Killing vector is discussed. When embedded into M-theory the compactification over a given Killing vector gives intersecting 6-branes as IIA configuration and we argue that membrane instantons may resolve the curvature singularity.