T-duality invariant effective actions at orders α ′, α ′ 2

Abstract

We use compatibility of the D-dimensional effective actions for diagonal metric and for dilaton with the T-duality when theory is compactified on a circle, to find the D-dimensional couplings of curvatures and dilaton as well as the higher derivative corrections to the (D − 1)-dimensional Buscher rules at orders α′ and α′². We observe that the T-duality constraint on the effective actions fixes the covariant effective actions at each order of α′ up to field redefinitions and up to an overall factor. Inspired by these results, we speculate that the D-dimensional effective actions at any order of α′ must be consistent with the standard Buscher rules provided that one uses covariant field redefinitions in the corresponding reduced (D − 1)-dimensional effective actions. This constraint may be used to find effective actions at all higher orders of α′.