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Using the superspace formalism, we compute for the two-dimensional N=1supersymmetric non-linear $\sigma$-model, the order $(\alpha^{\prime})^{2}$$(R_{mnpq})^2$ (three-loop) correction to the central charge via the operatorproduct expansion of the supercurrent with itself. The contribution vanishes,in agreement with previous results obtained from the usual $\sigma$-model$\beta$-function approach.Comment: 10 pp. + 1 uuencoded figur

OPE’s and the dilaton β function for the two-dimensionalN=1 supersymmetric nonlinear σ model