Local G 2-manifolds, Higgs bundles and a colored quantum mechanics

Abstract

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.

Keywords

• M-Theory
• Nonperturbative Effects
• Sigma Models
• Supersymmetric Gauge Theory