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

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.

41 pages, 2 figures

References in corpus (7)

• Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Derivation of Calabi-Yau Crystals from Chern-Simons Gauge Theory
• Brownian Motion, Chern-Simons Theory, and 2d Yang-Mills
• Chern-Simons Theory in Lens Spaces from 2d Yang-Mills on the Cylinder
• Universal Correlators from Geometry
• Large N limit of 2D Yang-Mills Theory and Instanton Counting

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• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Discrete and oscillatory Matrix Models in Chern-Simons theory
• Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory
• Interacting Particles on the Line and Dunkl Intertwining Operator of Type A: Application to the Freezing Regime
• Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model
• A Note on Knot Invariants and q-Deformed 2d Yang-Mills
• Localization for Wilson Loops in Chern-Simons Theory
• Knot invariants and Calabi-Yau crystals
• Large N Expansion of q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras
• Matrix models and stochastic growth in Donaldson-Thomas theory
• A Diffusion Model for SU(N) QCD Screening
• Surface-Invariants in 2D Classical Yang-Mills Theory
• Wilson punctured network defects in 2D q-deformed Yang-Mills theory
• Chern-Simons theory, exactly solvable models and free fermions at finite temperature
• Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
• Veneziano Amplitudes, Spin Chains and String Models