New $G_2$-conifolds in $M$-theory and their Field Theory Interpretation

TL;DR

This paper explores new $G_2$-holonomy manifolds in M-theory derived from circle bundles over Calabi-Yau cones, revealing dualities with gauge theories and supporting the geometric transitions through physical checks.

Contribution

It introduces a method to construct and analyze a broad class of $G_2$-holonomy orbifolds using Foscolo-Haskins-Nordstr"om's theorem, linking them to gauge theory dualities.

Findings

Construction of new $G_2$-holonomy orbifolds from circle bundles.

Identification of gauge theory duals in the IR for these backgrounds.

Physical checks support the proposed gauge/gravity duality.

Abstract

A recent theorem of Foscolo-Haskins-Nordstr\"om which constructs complete $G_2$-holonomy orbifolds from circle bundles over Calabi-Yau cones can be utilised to construct and investigate a large class of generalisations of the $M$-theory flop transition. We see that in many cases a UV perturbative gauge theory appears to have an infrared dual described by a smooth $G_2$-holonomy background in $M$-theory. Various physical checks of this proposal are carried out affirmatively.