Discrete and oscillatory Matrix Models in Chern-Simons theory

TL;DR

This paper introduces discrete and oscillatory matrix models for Chern-Simons theory, using orthogonal polynomials, and explores their implications for q-deformed 2dYM and N=1 gauge theories.

Contribution

It develops new discrete and oscillatory matrix models for Chern-Simons theory based on orthogonal polynomial properties, extending existing relationships and providing new insights.

Findings

Proves the relationship between Chern-Simons theory and q-deformed 2dYM.

Shows the equivalence of different Chern-Simons matrix models.

Provides a new perspective on superpotential equivalences in N=1 gauge theories.

Abstract

We derive discrete and oscillatory Chern-Simons matrix models. The method is based on fundamental properties of the associated orthogonal polynomials. As an application, we show that the discrete model allows to prove and extend the recently found relationship between Chern-Simons theory and q-deformed 2dYM. In addition, the equivalence of the Chern-Simons matrix models gives a complementary view on the equivalence of effective superpotentials in N=1 gauge theories.