Phases of supersymmetric gauge theories from M-theory on G_2 manifolds

TL;DR

This paper explores the phases of N=1 SU(2) gauge theories derived from M-theory on G_2 manifolds, analyzing geometric transitions and phase changes related to the topology of the compactification space.

Contribution

It extends the understanding of gauge theory phases by connecting them to specific geometric transitions in G_2 manifolds with orbifold constructions.

Findings

Identification of phase transitions via geometric S^3 flops for b_1=0

Realization of Coulomb and non-Abelian phases through desingularization for b_1=1

Description of extremal transitions at conifold points involving wrapped membranes

Abstract

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 generalizes to compact manifolds the study of the phase transition from the non-Abelian to the confining phase through geometrical S^3 flops. For b_1=1, the non-Abelian and Coulomb phases are realized, where the latter arises by desingularization of the fixed point set, while an S^2 x S^1 flop occurs. In addition, an extremal transition between G_2 spaces can take place at conifold points of the CY moduli space where unoriented membranes wrapped on CP^1 and RP^2 become massless.