Integrable sigma models on Riemann surfaces

We consider quantum aspects of a class of generalized Gross-Neveu models, which in special cases reduce to sigma models. We show that, in the case of gauged models, an admissible gauge is $A_{\mu }=0$, which is a direct analogue of the conformal gauge in string models. Chiral anomalies are a gauge counterpart of the Weyl anomaly, and are required to vanish. Topological effects on the worldsheet lead to an integration over moduli spaces of connections on a Riemann surface. This is an initial step in studying the effects of worldsheet geometry and topology in integrable sigma models.