WZW fusion rings in the limit of infinite level

WZW fusion rings in the limit of infinite level

Commun.Math.Phys. 185 (1997) 641-670 We show that the WZW fusion rings at finite levels form a projective system with respect to the partial ordering provided by divisibility of the height, i.e. the level shifted by a constant. From this projective system we obtain WZW fusion rings in the limit of i...

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Hauptverfasser: Fuchs, J"urgen, Schweigert, Christoph
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Physics - High Energy Physics - Theory
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description Commun.Math.Phys. 185 (1997) 641-670 We show that the WZW fusion rings at finite levels form a projective system with respect to the partial ordering provided by divisibility of the height, i.e. the level shifted by a constant. From this projective system we obtain WZW fusion rings in the limit of infinite level. This projective limit constitutes a mathematically well-defined prescription for the `classical limit' of WZW theories which replaces the naive idea of `sending the level to infinity'. The projective limit can be endowed with a natural topology, which plays an important role for studying its structure. The representation theory of the limit can be worked out by considering the associated fusion algebra; this way we obtain in particular an analogue of the Verlinde formula.
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title WZW fusion rings in the limit of infinite level
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