Fusion rules of chiral algebras

Abstract

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.

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

References in corpus (2)

• Null vectors of the W_3 algebra
• A2 Toda theory in reduced WZNW framework and the representations of the W algebra

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• Duality in N=2 minimal model holography
• An Introduction to Conformal Field Theory
• Correlators of the symmetric product orbifold
• Bosonic Ghosts at $c=2$ as a Logarithmic CFT
• Fusion of twisted representations
• Unitarity of rational N=2 superconformal theories
• Fusion rules for the logarithmic $N=1$ superconformal minimal models II: including the Ramond sector
• Fusion rules for the logarithmic $N=1$ superconformal minimal models I: the Neveu-Schwarz sector
• Fusion in the W_3 algebra
• Obstructions and lines of marginal stability from the world-sheet