  New heterotic modular invariants are found using the level-rank duality of
affine Kac-Moody algebras. They provide strong evidence for the consistency of
an infinite list of heterotic Wess-Zumino-Witten (WZW) conformal field
theories. We call the basic construction the dual-flip, since it flips
chirality (exchanges left and right movers) and takes the level-rank dual. We
compare the dual-flip to the method of conformal subalgebras, another way of
constructing heterotic invariants. To do so, new level-one heterotic invariants
are first found; the complete list of a specified subclass of these is
obtained. We also prove (under a mild hypothesis) an old conjecture concerning
exceptional $A_{r,k}$ invariants and level-rank duality.
