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

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.

70 pages, 16 figures, JHEP version

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Cited by in corpus (6)

• Reflections on the Matter of 3d $\mathcal{N}=1$ Vacua and Local $Spin(7)$ Compactifications
• A 5d perspective on the compactifications of 6d SCFTs to 4d $\mathcal{N}=1$ SCFTs
• Evidence for an Algebra of ${\mathbf{G}}_2$ Instantons
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• Neutrino mass matrices from localization in M-theory on $G_2$ orbifold