Abstract
Chiral matter coupling to two-dimensional quantum gravity is analyzed in the light-cone gauge. This theory exhibits both conformal and gravitational anomalies. The anomalous Ward identities are integrated and yield recursion relations among the correlation functions. An underlying SL(2, ℝ) × U(1) current algebra is revealed. Exact formula for the SL(2, ℝ) central charge and a relation connecting scaling dimensions and spin of fields are derived. The exact results and the renormalization of the U(1) charge of the fermion field are checked to one-loop order.
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