Local $G_2$-Manifolds, Higgs Bundles and a Colored Quantum Mechanics

TL;DR

This paper explores the relationship between M-theory on local G2-manifolds, Higgs bundles, and colored quantum mechanics, revealing how M2-brane instantons influence 4d superpotentials through a novel quantum mechanical perspective.

Contribution

It introduces a new correspondence between M2-brane instantons and colored quantum mechanics, providing a method to compute 4d superpotentials from 7d gauge theories.

Findings

M2-brane instantons correspond to instantons in colored quantum mechanics

Localization techniques compute contributions to 4d superpotential

Analysis of non-split Higgs bundles reveals their 4d spectrum

Abstract

M-theory on local $G_2$-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered $G_2$-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.