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On quantum gauge theories in two dimensions. (English) Zbl 0762.53063

Summary: Two dimensional quantum Yang-Mills theory is studied from three points of view: (i) by standard physical methods; (ii) by relating it to the large \(k\) limit of three dimensional Chern-Simons theory and two dimensional conformal field theory; (iii) by relating its weak coupling limit to the theory of Reidemeister-Ray-Singer torsion. The results obtained from the three points of view agree and give formulas for the volumes of the moduli spaces of representations of fundamental groups of two dimensional surfaces.

MSC:

53Z05 Applications of differential geometry to physics
81T13 Yang-Mills and other gauge theories in quantum field theory
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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