Local G2-manifolds, Higgs bundles and a colored quantum mechanics

Abstract

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.

Snowmass White Paper: String Theory and Particle Physics

“…M-theory compactifications on seven-manifolds with G 2 holonomy also give rise to large ensembles of 4d N = 1 vacua, where singularities at codimension 4, 6, and 7, encode the structure of gauge groups, non-chiral matter, and chiral matter, respectively; see [250] for an early review. More recently, constructions of so-called twisted connected sums [251] have given rise to millions of G 2 manifolds [252], which have been the subject of numerous physics studies in compact twisted connected sums [135,[253][254][255][256][257][258][259], and related Higgs bundle constructions [260][261][262][263][264]. For some recent progress on singular non-compact G 2 constructions and studies on gauge dynamics there, see [265,266].…”

Reflections on the Matter of 3d $\mathcal{N} = 1$ Vacua and Local $Spin(7)$ Compactifications

“…In this Appendix, we motivate the appearance of the twisted differential operator in the Spin(7) superpotential and 7d Dirac equation twisted on M 4 by formulating the supersymmetric quantum mechanics (SQM) of the Euclidean M2-Branes in the Spin(7) space is similar in spirit to references [17,18,100] for local G 2 models. We mainly focus on the case where we have the most concrete results, i.e.…”

Superconformal algebras for generalized Spin(7) and G2 connected sums

“…This can be done for the orbifold I, with the external circle given by the coordinate x 8 . 20 A realization of the diamond of algebras can be obtained and upon studying the action of T-dualities on it we find: (1,3,5,7), (2, 4, 5, 7)}.…”