ON GRAVITATIONAL DRESSING OF 2D FIELD-THEORIES IN CHIRAL GAUGE

After giving a pedagogical review of the chiral gauge approach to 2D g ravity, with particular emphasis on the derivation of the gravitationa l Ward identities, we discuss in some detail the interpretation of mat ter correlation functions coupled to gravity in chiral gauge. We argue that in chiral gauge no explicit gravitational dressing factor, analo gue to the Liouville exponential in conformal gauge, is necessary for left-right symmetric matter operators. In particular, we examine the g ravitationally dressed four-point correlation function of products of left and right fermions, We solve the corresponding gravitational Ward identity exactly: in the presence of gravity this four-point function exhibits a logarithmic short-distance singularity, instead of the pow er-law singularity in the absence of gravity. This rather surprising e ffect is non-perturbative in the gravitational coupling and is a sign for logarithms in the gravitationally dressed operator product expansi ons. We also discuss some perturbative evidence that the chiral Gross- Neven model may remain integrable when coupled to gravity.