Supergravity dressing of β-functions in N = 1 and N = 2 supersymmetric models

We discuss the dressing of one-loop σ-model β-functions by induced supergravity, for both N = 1 and N = 2 supersymmetric theories. We obtain exact results by a superconformal gauge argument, and verify them in the semi-classical limit by explicit perturbative calculations in the light-cone gauge. We find that for N = 2 theories there is no dressing of the one-loop β-functions.