Abstract
Simple currents have been used previously to construct various examples of modular invariant partition functions for given rational conformal field theories. In this paper we present for a large class of such theories (namely those with a center that decomposes into factors Z p ,p prime) thecomplete set of modular invariants that can be obtained with simple currents. In addition to the fusion rule automorphisms classified previously forany center, this includes all possible left-right combinations of all possible extensions of the chiral algebra that can be obtained with simple currents, for all possible current-current monodromies. Formulas for the number of invariants of each kind are derived. Although the number of invariants in each of these subsets depends on the current-current monodromies, the total number of invariants depends rather surprisingly only onp and the number ofZ p factors.
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Communicated by K. Gawedzki
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Gato-Rivera, B., Schellekens, A.N. Complete classification of simple current modular invariants for RCFT's with a center (Z p )k . Commun.Math. Phys. 145, 85–121 (1992). https://doi.org/10.1007/BF02099282
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DOI: https://doi.org/10.1007/BF02099282