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 Zp,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 ofZp factors.
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