Quantum Geometries of $A_{2}$

Abstract

We solve $\mathcal{N}=1$ supersymmetric $A_{2}$ type $U(N)\times U(N)$ matrix models obtained by deforming $\mathcal{N}=2$ with symmetric tree level superpotentials of any degree exactly in the planar limit. These theories can be geometrically engineered from string theories by wrapping D-branes over Calabi-Yau threefolds and we construct the corresponding exact quantum geometries.