nameki M-theory compactified on G 2 -holonomy manifolds results in 4d N = 1 supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained from a partially twisted 7d super Yang-Mills theory on a supersymmetric three-cycle M 3 . We derive the BPS equations and find the massless spectrum for both abelian and non-abelian gauge groups in 4d. The mathematical tool that allows us to determine the spectrum is Morse theory, and more generally Morse-Bott theory. The latter generalization allows us to make contact with twisted connected sum (TCS) G 2 -manifolds, which form the largest class of examples of compact G 2 -manifolds. M-theory on TCS G 2 -manifolds is known to result in a non-chiral 4d spectrum. We determine the Higgs bundle for this class of G 2 -manifolds and provide a prescription for how to engineer singular transitions to models that have chiral matter in 4d. arXiv:1812.06072v2 [hep-th]

We study the holographic dual to cc-extremization for 2d (0,2)(0,2) superconformal field theories (SCFTs) that have an AdS_33 dual realized in Type IIB with varying axio-dilaton, i.e. F-theory. M/F-duality implies that such AdS_33 solutions can be mapped to AdS_22 solutions in M-theory, which are holographically dual to superconformal quantum mechanics (SCQM), obtained by dimensional reduction of the 2d SCFTs. We analyze the corresponding map between holographic cc-extremization in F-theory and \mathcal{I}ℐ-extremization in M-theory, where in general the latter receives corrections relative to the F-theory result.