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

de Haro, Sebastian

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

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de Haro, Sebastian
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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de Haro, S. (2005). Chern-Simons Theory, 2d Yang-Mills, and Lie Algebra Wanderers. Nuclear Physics B, 730(3), 312-351.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4EA8-1

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.