Chern-Simons Theory, 2d Yang-Mills, and Lie Algebra Wanderers

Details Chern-Simons Theory, 2d Yang-Mills, and Lie Algebra Wanderers Chern-Simons Theory, 2d Yang-Mills, and Lie Algebra Wanderers

2004-12-11

arxiv.org/abs/hep-th/0412110v2

Nucl.Phys. B730 (2005) 312-351

Physics

High Energy Physics

High Energy Physics - Theory

41 pages, 2 figures

Scientific paper

10.1016/j.nuclphysb.2005.09.009

We work out the relation between Chern-Simons, 2d Yang-Mills on the cylinder, and Brownian motion. We show that for the unitary, orthogonal and symplectic groups, various observables in Chern-Simons theory on S^3 and lens spaces are exactly given by counting the number of paths of a Brownian particle wandering in the fundamental Weyl chamber of the corresponding Lie algebra. We construct a fermionic formulation of Chern-Simons on $S^3$ which allows us to identify the Brownian particles as B-model branes moving on a non-commutative two-sphere, and construct 1- and 2-matrix models to compute Brownian motion ensemble averages.

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