Matrix model as a mirror of Chern-Simons theory

Abstract

Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as tens spaces reduces to a novel class of hermitean 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 G(2) manifolds) this leads to engineering and solving F-terms for N = 1 supersymmetric gauge theories with superpotentials involving certain multi-trace operators.