THE RANK-4 HETEROTIC MODULAR INVARIANT PARTITION-FUNCTIONS

In this paper, we develop several general techniques to investigate mo dular invariants of conformal field theories whose algebras of the hol omorphic and anti-holomorphic sectors are different. As an application , we find all such ''heterotic'' WZNW physical invariants of (horizont al) rank four: there are exactly seven of these, two of which seem to be new. Previously, only those of rank less-than-or-equal-to 3 have be en completely classified. We also find all physical modular invariants for su(2)k1 x su(2)k2, for 22 > k1 > k2, and k1 = 28, k2 < 22, comple ting the classification of Ref. [9].