Mirror Symmetry and a $G_2$ Flop

TL;DR

This paper explores mirror symmetry applied to D-branes in Calabi-Yau geometries to understand $G_2$ flops in M-theory, deriving superpotentials and dual descriptions relevant for ${ m N}=1$ gauge theories.

Contribution

It introduces a method to derive superpotentials for M-theory on $G_2$ manifolds across all A-D-E cases, linking mirror symmetry to geometric engineering of ${ m N}=1$ gauge theories.

Findings

Derived superpotentials for M-theory on $G_2$ manifolds.

Identified dual descriptions of the $G_2$ flop.

Provided a geometric engineering framework for ${ m N}=1$ gauge theories.

Abstract

By applying mirror symmetry to D-branes in a Calabi-Yau geometry we shed light on a $G_2$ flop in M-theory relevant for large $N$ dualities in ${\cal N}=1$ supersymmetric gauge theories. Furthermore, we derive superpotential for M-theory on corresponding $G_2$ manifolds for all A-D-E cases. This provides an effective method for geometric engineering of ${\cal N}=1$ gauge theories for which mirror symmetry gives exact information about vacuum geometry. We also find a number of interesting dual descriptions.