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arXiv · hep-th/9911239

The formulae of Kontsevich and Verlinde from the perspective of the Drinfeld double

C. Klimcik
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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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C. Klimcik. 1999-12-13. The formulae of Kontsevich and Verlinde from the perspective of the Drinfeld double. https://doi.org/10.1007/s002200000355

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