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

TL;DR

This paper calculates higher-order corrections to the central charge in a 2D N=1 supersymmetric non-linear sigma model using superspace formalism, confirming previous results that these corrections vanish.

Contribution

It provides a three-loop order calculation of the $( ext{Riemann tensor})^2$ correction to the central charge using superspace, extending prior beta-function analyses.

Findings

The $( ext{Riemann tensor})^2$ correction vanishes at three-loop order.

Results agree with previous beta-function approach findings.

Supports the consistency of superspace formalism in superstring effective actions.

Abstract

Using the superspace formalism, we compute for the two-dimensional N=1 supersymmetric non-linear $\sigma$-model, the order $(\alpha^{\prime})^{2}$ $(R_{mnpq})^2$ (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 $\sigma$-model $\beta$-function approach.