Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model

Richard J. Szabo, Miguel Tierz

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22 Citations (Scopus)


We derive some new relationships between matrix models of Chern-Simons gauge theory and of two-dimensional Yang-Mills theory. We show that q-integration of the Stieltjes-Wigert matrix model is the discrete matrix model that describes q-deformed Yang-Mills theory on S2. We demonstrate that the semiclassical limit of the Chern-Simons matrix model is equivalent to the Gross-Witten model in the weak-coupling phase. We study the strong-coupling limit of the unitary Chern-Simons matrix model and show that it too induces the Gross-Witten model, but as a first-order deformation of Dyson's circular ensemble. We show that the Sutherland model is intimately related to Chern-Simons gauge theory on S3, and hence to q-deformed Yang-Mills theory on S2. In particular, the ground-state wavefunction of the Sutherland model in its classical equilibrium configuration describes the Chern-Simons free energy. The correspondence is extended to Wilson line observables and to arbitrary simply laced gauge groups. © 2010 IOP Publishing Ltd.

Original languageEnglish
Article number265401
JournalJournal of Physics A: Mathematical and Theoretical
Issue number26
Publication statusPublished - 2010


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