Matrix Model as a Mirror of Chern-Simons Theory

TL;DR

This paper demonstrates that Chern-Simons theory on specific manifolds can be represented by Hermitian matrix models via mirror symmetry, enabling computations of topological string amplitudes and supersymmetric gauge theory F-terms.

Contribution

It introduces a novel matrix model formulation of Chern-Simons theory on lens spaces and connects it to topological string amplitudes and supersymmetric gauge theories.

Findings

Matrix models reproduce Chern-Simons theory results.

Large N dualities compute topological string amplitudes.

Applications to N=1 supersymmetric gauge theories with superpotentials.

Abstract

Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of Chern-Simons theory. Moreover, large N dualities in this context lead to computation of all genus A-model topological amplitudes on toric Calabi-Yau manifolds in terms of matrix integrals. In the context of type IIA superstring compactifications on these Calabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2 manifolds) this leads to engineering and solving F-terms for N=1 supersymmetric gauge theories with superpotentials involving certain multi-trace operators.