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arXiv · 2009.07136

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

Max Hubner
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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.

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Max Hubner. 2020-09-15. Local $G_2$-Manifolds, Higgs Bundles and a Colored Quantum Mechanics. https://doi.org/10.1007/jhep05(2021)002

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