SIMPLE CURRENTS VERSUS ORBIFOLDS WITH DISCRETE TORSION - A COMPLETE CLASSIFICATION

We give a complete classification of all simple current modular invari ants, extending previous results for (Z(p))k to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbi fold techniques to this end, we find a one-to-one correspondence betwe en simple current invariants and subgroups of the center with discrete torsions. As a by-product, we prove the conjectured monodromy indepen dence of the total number of such invariants. The orbifold approach wo rks in a straightforward way for symmetries of odd order, but some mod ifications are required to deal with symmetries of even order. With th ese modifications the orbifold construction with discrete torsion is c omplete within the class of simple current invariants. Surprisingly, t here are cases where discrete torsion is a necessity rather than a pos sibility.