Higher-derivative couplings and torsional Riemann curvature

TL;DR

This paper demonstrates that higher-derivative couplings in string theory involving metric, B-field, and dilaton can be expressed using torsional Riemann curvature and torsion tensor, aligning with known results from S-matrix calculations.

Contribution

It shows how to rewrite tree-level higher-derivative couplings in terms of torsional Riemann curvature, unifying recent T-duality results with established S-matrix findings.

Findings

Couplings at order α'^2 include R^3, H^2 R^2, H^6 structures.

Couplings at order α'^3 include R^4 and H^2 R^3 structures.

Replacing R with ordinary Riemann curvature reproduces known S-matrix couplings.

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