ﻻ يوجد ملخص باللغة العربية
M-theory compactified on $G_2$-holonomy manifolds results in 4d $mathcal{N}=1$ 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.
We consider the non-perturbative superpotential for a class of four-dimensional $mathcal N=1$ vacua obtained from M-theory on seven-manifolds with holonomy $G_2$. The class of $G_2$-holonomy manifolds we consider are so-called twisted connected sum (
We study the four-dimensional low energy effective $mathcal{N}=1$ supergravity theory of the dimensional reduction of M-theory on $G_2$-manifolds, which are constructed by Kovalevs twisted connected sum gluing suitable pairs of asymptotically cylindr
We consider M-theory on compact spaces of G_2 holonomy constructed as orbifolds of the form (CY x S^1)/Z_2 with fixed point set Sigma on the CY. This describes N=1 SU(2) gauge theories with b_1(Sigma) chiral multiplets in the adjoint. For b_1=0, it g
We prove that there is no parity anomaly in M-theory in the low-energy field theory approximation. Our approach is computational. We determine generators for the 12-dimensional bordism group of pin manifolds with a w_1-twisted integer lift of w_4; th
This is a review article on some applications of generalised parabolic structures to the study of torsion free sheaves and $L$-twisted Hitchin pairs on nodal curves. In particular, we survey on the relation between representations of the fundamental