Quantum Geometries of $A_{2}$

TL;DR

This paper exactly solves supersymmetric $A_2$ matrix models in the planar limit, constructs their quantum geometries, and connects these results to string theory via Calabi-Yau threefolds.

Contribution

It provides an exact solution for $ =1$ supersymmetric $A_2$ matrix models and constructs their quantum geometries, extending previous work to arbitrary superpotential degrees.

Findings

Exact solutions for $ =1$ supersymmetric $A_2$ matrix models.

Construction of corresponding quantum geometries.

Connection to string theory via Calabi-Yau threefolds.

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.