In this paper, we develop several general techniques to investigate modular
invariants of conformal field theories whose algebras of the holomorphic and
anti-holomorphic sectors are different. As an application, we find all such
``heterotic'' WZNW physical invariants of (horizontal) rank four: there are
exactly seven of these, two of which seem to be new. Previously, only those of
rank β€3 have been completely classified. We also find all physical modular
invariants for su(2)k1ββΓsu(2)k2ββ, for 22>k1β>k2β, and k1β=28,
k2β<22, completing the classification of ref.{} \SUSU.Comment: 25 pp., plain te