Local supersymmetry, superconformal algebra in two dimensions and strings in background fields

Abstract

We show how the D=2 superconformal algebra emerges from the two-dimensional supergravity and develop a tensor calculus which is useful for constructing invariant actions. We apply this to the supersymmetric nonlinear σ-model in a dilaton background and show that the proper treatment of the auxiliary fields leads to a dilaton dependent four-fermion coupling. Due to this term a nonvanishing dilaton contribution to the metric ß-function emerges at the three-loop order. To this order Ricci flat spaces seem to be consistent with superconformal invariance if the dilaton background satisfies ∇ μ ∇ ν φ=0.