O(ALPHA'3) BETA FUNCTIONS IN THE SUPERSYMMETRIC SIGMA-MODEL WITH DILATON

We calculate the O(α′3) renormalization group beta functions in the N=1 supersymmetric σ-model in the presence of metric and dilaton backgrounds. At this loop order both metric and dilaton beta functions are found to depend nontrivially on the dilaton field φ being vanishing only if the dilaton satisfies {down triangle, open}μ{down triangle, open}νφ=0. By employing the Curci-Paffuti equation it can be further shown that Rμν=0, {down triangle, open}μ{down triangle, open}νφ=0 are backgrounds consistent with conformal invariance up to O(α′3). Dilaton fields in a Minkowski space linearly dependent on the space-time components, whose importance has been advocated in the literature, belong to this particular class of backgrounds. © 1990.