Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-01-16
Nucl.Phys. B473 (1996) 323-366
Physics
High Energy Physics
High Energy Physics - Theory
Phyzzx, 53 pages 1 uuencoded figure Arrow in figure corrected; Forgotten acknowledment to funding organization added; DESY pre
Scientific paper
10.1016/0550-3213(96)00247-7
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.
Fuchs J"urgen
Schellekens Bert
Schweigert Christoph
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