G_2 Holonomy, Mirror Symmetry and Phases of N=1 SYM

TL;DR

This paper explores the phase structure and quantum moduli space of four-dimensional N=1 super Yang-Mills theories on D6-branes, revealing how different gauge group configurations are interconnected through dualities and monopole condensation.

Contribution

It provides a detailed analysis of the quantum moduli space of these theories, incorporating duality relations and the role of complex curves in IIB string theory.

Findings

Quantum moduli space consists of multiple branches with different gauge symmetries.

Branches are connected at monopole condensation points.

The study links various gauge theories with different product groups.

Abstract

We study the phase structure of four-dimensional N=1 super Yang-Mills theories realized on D6-branes wrapping the RP^3 of a Z_2 orbifold of the deformed conifold. The non-trivial fundamental group of RP^3 allows for the gauge group to be broken to various product groups by Z_2 Wilson lines. We study the classical moduli space of theories in various pictures related by dualities including an M-theory lift. The quantum moduli space is analyzed in a dual IIB theory, where a complex curve contained in the target space plays a key role. We find that the quantum moduli space is made up of several branches, characterized by the presence or absence of a low energy U(1) gauge symmetry, which are connected at points of monopole condensation. The resulting picture of the quantum moduli space shows how the various gauge theories with different product gauge groups are connected to one another.