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

Sebastian de Haro

doi:10.1016/j.nuclphysb.2005.09.009

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arXiv · hep-th/0412110

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

Sebastian de Haro

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Abstract

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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BibTeX RIS

Sebastian de Haro. 2005-09-09. Chern-Simons Theory, 2d Yang-Mills, and Lie Algebra Wanderers. https://doi.org/10.1016/j.nuclphysb.2005.09.009

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