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

  • Miguel TierzEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We solve for finite N the matrix model of supersymmetric U(N ) Chern-Simons theory coupled to N f fundamental and N f 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 N f , in terms of a single Hermite polynomial. This result also holds for more general matter content, involving matrix models with doublesine functions.

Keywords

Matrix Models Chern-Simons Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Departamento de Matemática, Grupo de Física Matemática, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal

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