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arXiv · hep-th/0609167

Chern-Simons matrix models and Stieltjes-Wigert polynomials

Yacine Dolivet·Miguel Tierz
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Abstract

Employing the random matrix formulation of Chern-Simons theory on Seifert manifolds, we show how the Stieltjes-Wigert orthogonal polynomials are useful in exact computations in Chern-Simons matrix models. We construct a biorthogonal extension of the Stieltjes-Wigert polynomials, not available in the literature, necessary to study Chern-Simons matrix models when the geometry is a lens space. We also discuss several other results based on the properties of the polynomials: the equivalence between the Stieltjes-Wigert matrix model and the discrete model that appears in q-2D Yang-Mills and the relationship with Rogers-Szego polynomials and the corresponding equivalence with an unitary matrix model. Finally, we also give a detailed proof of a result that relates quantum dimensions with averages of Schur polynomials in the Stieltjes-Wigert ensemble.

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Yacine Dolivet, Miguel Tierz. 2006-09-25. Chern-Simons matrix models and Stieltjes-Wigert polynomials. https://doi.org/10.1063/1.2436734

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