Renormalization Group Flows in Sigma–models Coupled to Two–dimensional Dynamical Gravity

We consider a bosonic σ–model coupled to two–dimensional gravity. In the semiclassical limit, c → −∞, we compute the gravity dressing of the β–functions at two–loop order in the matter fields. We find that the corrections due to the presence of dynamical gravity are not expressible simply in terms of a multiplicative factor as previously obtained at the one–loop level. Our result indicates that the critical points of the theory are nontrivially influenced and modified by the induced gravity. IFUM–528–FT May 1996 E–mail address: [email protected] E–mail address: [email protected] E–mail address: [email protected]