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

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

1999-11-29

arxiv.org/abs/hep-th/9911239v2

Commun.Math.Phys. 217 (2001) 203-228

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, LaTeX, references added

Scientific paper

10.1007/s002200000355

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 $\sigma$-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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