Effective actions from the conformal invariance conditions of bosonic σ-models with graviton and dilaton backgrounds

Abstract

We discuss generalised functional relations between the β-functions of bosonic σ-models propagating in graviton and dilaton backgrounds and field variations of the associated effective actions based on these backgrounds. We analyse the constraints on the possible form of the proportionality (non-degenerate) tensors, imposed by classical symmetries of the associated point-like action. As an application we derive the second order [O(α′)] effective action and we find that it is consistent with a ghost free combination for both fields. Moreover we show explicitly that this action is related to the one computed within the framework of string tree-amplitudes by field redefinitions.