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 $N_f$ 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 double-sine functions.

17 pages, v2: a paragraph added; final, published, version

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Cited by in corpus (7)

• Solvable Quantum Grassmann Matrices
• Polynomial solution of quantum Grassmann matrices
• 4d/2d $\to$ 3d/1d: A song of protected operator algebras
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Asymptotics of partition functions in a fermionic matrix model and of related $q$-polynomials