Higher-derivative couplings and torsional Riemann curvature

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 alpha('2 )and alpha(iota 3) that have been recently found by the T-duality, can be written in a particular scheme in terms of the torsional Riemann curvature R and the torsion tensor H. The couplings at order alpha('2) have structures R-3, (HR2)-R-2, H-6, and the couplings at order alpha(iota 3) have only structures R-4, (HR3)-R-2. Replacing R with the ordinary Riemann curvature, the couplings in the structure (HR3)-R-2 reproduce the couplings found in the literature by the S-matrix method.

Automated summary

This study shows that the tree-level couplings of the metric, B-field, and dilaton at certain orders can be expressed in terms of torsional Riemann curvature and torsion tensor. The findings support previous literature on couplings through the S-matrix method.