Higher-derivative couplings and torsional Riemann curvature

Abstract

Using the most general higher-derivative field redefinition for the closed spacetime manifolds, we show that the tree-level couplings of the metric, $B$-field and dilaton at orders ${\alpha }^{\prime 2}$ and ${\alpha }^{\prime 3}$ that have been recently found by the T-duality, can be written in a particular scheme in terms of the torsional Riemann curvature $\mathcal{R}$ and the torsion tensor $H$. The couplings at order ${\alpha }^{\prime 2}$ have structures ${\mathcal{R}}^3,H^2{\mathcal{R}}^2$, $H^6$, and the couplings at order ${\alpha }^{\prime 3}$ have only structures ${\mathcal{R}}^4$, $H^2{\mathcal{R}}^3$. Replacing $\mathcal{R}$ with the ordinary Riemann curvature, the couplings in the structure $H^2{\mathcal{R}}^3$ reproduce the couplings found in the literature by the S-matrix method.

18 pages, Latex file, no figure;v2: It is argued that the world-volume couplings can also be rewritten in terms of the torsional Riemann curvature

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