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

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

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4EA8-1 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4EA9-0
Genre: Journal Article

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0412110.pdf (Preprint), 378KB
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 Creators:
de Haro, Sebastian1, Author
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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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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Language(s): eng - English
 Dates: 2005
 Publication Status: Published in print
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 Identifiers: eDoc: 207104
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Title: Nuclear Physics B
Source Genre: Journal
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Pages: - Volume / Issue: 730 (3) Sequence Number: - Start / End Page: 312 - 351 Identifier: -