M-theory on local G₂-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G₂-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.

关于局部G ₂流形的M理论工程师4d最小超对称规范理论。我们考虑ALE纤维G ₂流形，并从部分扭曲的7d超对称Yang-Mills理论及其希格斯束的角度研究4d物理学。欧几里得M2振子实例归因于7d超对称Yang-Mills理论的非扰动效应，发现它与有色超对称量子力学的实例一一对应。我们通过有色量子力学中的局部化计算了M2磁子瞬子对有效7d描述中4d超势的贡献。此外，我们考虑非分裂的希格斯束，并分析其4d光谱。