Higher-derivative couplings and torsional Riemann curvature

Abstract

Abstract Using the most general higher-derivative field redefinitions for the closed spacetime manifolds, we show that the tree-level couplings of the metric, B-field and dilaton at orders α′2 and α′3 that have been recently found by the T-duality, can be written in a particular scheme in terms of the torsional Riemann curvature $$ \mathcal{R} $$ R and the torsion tensor H. The couplings at order α′2 have structures $$ \mathcal{R} $$ R 3, H2$$ \mathcal{R} $$ R 2, H6, and the couplings at order α′3 have only structures $$ \mathcal{R} $$ R 4, H2$$ \mathcal{R} $$ R 3. Replacing $$ \mathcal{R} $$ R with the ordinary Riemann curvature, the couplings in the structure H2$$ \mathcal{R} $$ R 3 reproduce the couplings found in the literature by the S-matrix method.