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arXiv · hep-th/9601078

A matrix S for all simple current extensions

J"urgen Fuchs·Bert Schellekens·Christoph Schweigert
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Abstract

A formula is presented for the modular transformation matrix S for any simple current extension of the chiral algebra of a conformal field theory. This provides in particular an algorithm for resolving arbitrary simple current fixed points, in such a way that the matrix S we obtain is unitary and symmetric and furnishes a modular group representation. The formalism works in principle for any conformal field theory. A crucial ingredient is a set of matrices S^J_{ab}, where J is a simple current and a and b are fixed points of J. We expect that these input matrices realize the modular group for the torus one-point functions of the simple currents. In the case of WZW-models these matrices can be identified with the S-matrices of the orbit Lie algebras that we introduced in a previous paper. As a special case of our conjecture we obtain the modular matrix S for WZW-theories based on group manifolds that are not simply connected, as well as for most coset models.

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J"urgen Fuchs, Bert Schellekens, Christoph Schweigert. 1996-02-15. A matrix S for all simple current extensions. https://doi.org/10.1016/0550-3213(96)00247-7

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