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- W2008348105 abstract "We give a derivation of the Verlinde formula for the Gk WZW model from Chern-Simons theory, without taking recourse to CFT, by calculating explicitly the partition function ZΣ×S1 of Σ × S1 with an arbitrary number of labelled punctures. By what is essentially a suitable gauge choice, ZΣ×S1 is reduced to the partition function of an abelian topological field theory on Σ (a deformation of non-abelian BF and Yang-Mills theory) whose evaluation is straightforward. This relates the Verlinde formula to the Ray-Singer torsion of Σ × S1. We derive the Gk/Gk model from Chern-Simons theory, proving their equivalence, and give an alternative derivation of the Verlinde formula by calculating the Gk/Gk path integral via a functional version of the Weyl integral formula. From this point of view the Verlinde formula arises from the corresponding jacobian, the Weyl determinant. Also, a novel derivation of the shift k → k + h is given, based on the index of the twisted Dolbeault complex." @default.
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- W2008348105 date "1993-11-01" @default.
- W2008348105 modified "2023-09-30" @default.
- W2008348105 title "Derivation of the Verlinde formula from Chern-Simons theory and the G/G model" @default.
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- W2008348105 doi "https://doi.org/10.1016/0550-3213(93)90538-z" @default.
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