Abstract:
A two dimensional gauge theory is canonically associated to every Drinfeld double. For particular doubles, the theory turns out to be e.g. the ordinary Yang–Mills theory, the G/G gauged WZNW model or the Poisson σ-model that underlies the Kontsevich quantization formula. We calculate the arbitrary genus partition function of the latter. The result is the q-deformation of the ordinary Yang–Mills partition function in the sense that the series over the weights is replaced by the same series over the q-weights. For q equal to a root of unity the series acquires the affine Weyl symmetry and its truncation to the alcove coincides with the Verlinde formula.
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Received: 10 December 1999 / Accepted: 8 October 2000
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Klimĉík, C. The Formulae of Kontsevich and Verlinde¶from the Perspective of the Drinfeld Double. Commun. Math. Phys. 217, 203–228 (2001). https://doi.org/10.1007/s002200000355
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DOI: https://doi.org/10.1007/s002200000355