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

Abstract

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.

15 pages; v2: references added

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• Physics and Mathematics of Calogero particles
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• Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
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• Unitary Chern-Simons matrix model and the Villain lattice action
• On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field
• Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex model
• Holographic Hierarchy in the Gaussian Matrix Model via the Fuzzy Sphere
• Chern-Simons theory encoded on a spin chain
• Matrix models and stochastic growth in Donaldson-Thomas theory
• Supersymmetric gauge theories, Coulomb gases and Chern-Simons matrix models
• On the Virasoro constraints for torus knots
• Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory