Chern-Simons matrix models and Stieltjes-Wigert polynomials

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dc.creatorDolivet, Yacine
dc.creatorTierz, Miguel
dc.date2006-09-25
dc.date.accessioned2026-07-07T11:27:44Z
dc.date.available2026-07-07T11:27:44Z
dc.descriptionEmploying 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.
dc.description25 pages, AMS-LaTex
dc.identifierhttps://arxiv.org/abs/hep-th/0609167
dc.identifierhttp://arxiv.org/abs/hep-th/0609167
dc.identifierJ.Math.Phys.48:023507,2007
dc.identifierdoi:10.1063/1.2436734
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/196231
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleChern-Simons matrix models and Stieltjes-Wigert polynomials
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