Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials

Abstract

We solve for finite N the matrix model of supersymmetric U(N) Chern-Simons theory coupled to Nf fundamental and Nf anti-fundamental chiral multiplets of R-charge 1/2 and of mass m, by identifying it with an average of inverse characteristic polynomials in a Stieltjes-Wigert ensemble. This requires the computation of the Cauchy transform of the Stieltjes-Wigert polynomials, which we carry out, finding a relationship with Mordell integrals, and hence with previous analytical results on the matrix model. The semiclassical limit of the model is expressed, for arbitrary Nf, in terms of a single Hermite polynomial. This result also holds for more general matter content, involving matrix models with doublesine functions.