It is shown that conformal matter with $c_{ \ssc L}\not=c_{ \ssc R}$ can be consistently coupled to two-dimensional `frame' gravity. The theory is quantized, following David, and Distler and Kawai, using the derivation of their { \it ansatz} due to Mavromatos and Miramontes, and D'Hoker and Kurzepa. New super-selection rules are found by requiring SL(2,{ \bf C}) invariance of correlation functions on the plane. There is no analogue of the $c=1$ barrier found in non-chiral non-critical strings. A non-critical heterotic string is constructed---it has 744 states in its spectrum, transforming in the adjoint representation of $(E_8)^3.$ Correlation functions are calculated in this example.
Categories: hep-th