String effective actions from sigma-model conformal anomalies

Abstract

We consider the sigma model describing a closed bosonic string in the presence of graviton, anti-symmetric tensor and dilaton background fields. Using previous results for the metric and anti-symmetric tensor two-loop beta-functions, we derive the dilaton beta-function and obtain the full set of conditions for conformal invariance to the same order. We show that these conditions can be derived from any one of a family of space-time effective actions. After taking field redefinitions into account our action agrees with that obtained by Metsaev and Tseytlin.