2010/03/29 by Richard J. Szabo, Miguel Tierz · 1 citation
Physics and Astronomy · Mathematics · #hep-th #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/43/26/265401
published as J.Phys.A43:265401,2010 · 15 pages; v2: references added
arxiv created 2010/03/29 · arxiv updated 2015/05/18
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 the 2-sphere. 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 the 3-sphere, and hence to q-deformed Yang-Mills theory on the 2-sphere. 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.