Beta functions and central charge of supersymmetric sigma models with torsion

We present a method for the computation of the renormalization group β-functions and the central charge in two-dimensional supersymmetric sigma models in a gravitational background. The two-loops results are exhibited. We use the Pauli-Villars regularization which preserves supersymmetry and permits an unambiguous treatment of the model with torsion. The central charge we derive for a general manifold is in agreement with the expression found on group manifolds.