Fusion rules of chiral algebras

Details Fusion rules of chiral algebras Fusion rules of chiral algebras

1993-09-20

arxiv.org/abs/hep-th/9309105v2

Nucl.Phys. B417 (1994) 130-150

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, Latex, DAMTP-93-56 (minor corrections only)

Scientific paper

10.1016/0550-3213(94)90540-1

Recently (hep-th/9307183) we showed that for the case of the WZW- and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral algebras. We define the tensor product of conformal field theory in the general case and prove that it is associative and symmetric up to equivalence. We also determine explicitly the action of the chiral algebra on this tensor product. In the second part of the paper we demonstrate that this framework provides a powerful tool for calculating restrictions for the fusion rules of chiral algebras. We exhibit this for the case of the $W_{3}$-algebra and the $N=1$ and $N=2$ NS superconformal algebras.

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