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.
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Tierz, M. Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials. J. High Energ. Phys. 2016, 168 (2016). https://doi.org/10.1007/JHEP04(2016)168
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DOI: https://doi.org/10.1007/JHEP04(2016)168
Keywords
- Matrix Models
- Chern-Simons Theories