OPE's and the Dilaton Beta-Function for the 2-D N=1 Supersymmetric Non-Linear $σ$-Model

Abstract

Using the superspace formalism, we compute for the two-dimensional N=1 supersymmetric non-linear $σ$-model, the order $(α^{\prime})^{2}$ $(R_{mnpq})^2$ (three-loop) correction to the central charge via the operator product expansion of the supercurrent with itself. The contribution vanishes, in agreement with previous results obtained from the usual $σ$-model $β$-function approach.