Intersecting 6-branes from new 7-manifolds with G_2 holonomy

TL;DR

The work constructs a novel $G_2$ holonomy metric as an $R^3$-bundle over a two–isometry quaternionic base and analyzes its fixed-point set to realize intersecting D6-branes after Type IIA reduction. The base space is explicitly engineered via a pair of cubic polynomials $P(p)$ and $Q(q)$, yielding a rich fixed-point structure that includes co-dimension-4 loci corresponding to D6-branes; by tuning roots and Killing vectors, the authors obtain a three-stack D6-brane configuration and discuss quantization conditions that guarantee consistent $U(1)$ actions. The Type IIA reduction produces a concrete ten-dimensional background with a dilaton and RR/NS-NS fields, illustrating how the brane content emerges from M-theory geometry without introducing extra NS5-branes. Collectively, the results advance geometric engineering of four-dimensional $\mathcal{N}=1$ theories from $G_2$ manifolds and illuminate connections to weighted projective spaces and intersecting brane models. The work sets the stage for further exploration of gauge-theory content, brane intersections, and dual descriptions in this geometric framework.

Abstract

We discuss a new family of metrics of 7-manifolds with G_2 holonomy, which are R^3 bundles over a quaternionic space. The metrics depend on five parameters and have two Abelian isometries. Certain singularities of the G_2 manifolds are related to fixed points of these isometries; there are two combinations of Killing vectors that possess co-dimension four fixed points which yield upon compactification only intersecting D6-branes if one also identifies two parameters. Two of the remaining parameters are quantized and we argue that they are related to the number of D6-branes, which appear in three stacks. We perform explicitly the reduction to the type IIA model.