Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials
- 90 Downloads
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.
KeywordsMatrix Models Chern-Simons Theories
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.
- P.J. Forrester, Log-gases and random matrices, Princeton University Press (2010).Google Scholar
- P. Deift, Orthogonal Polynomials and Random Matrices: a Riemann-Hilbert Approach, AMS Courant Lecture Notes (2000).Google Scholar
- G. Szegö, Orthogonal Polynomials, fourth edition, Colloquium Publications of the American Mathematical Society, Volume XXIII (1975), section 2.7.Google Scholar
- M.K. Atakishiyeva, N.M. Atakishiyev and T.H. Koornwinder, q-Extension of Mehta’s eigenvectors of the finite Fourier transform for q a root of unity, J. Phys. A Math. Gen. 42 (2009) 454004 [arXiv:0811.4100].