Generalized Riemann curvature corrections to type II supergravity

TL;DR

This paper refines the higher-order curvature corrections in type II supergravity by ensuring T-duality invariance and consistency with superstring S-matrix elements, leading to a corrected Lagrangian involving generalized Riemann curvature.

Contribution

It introduces T-duality invariant couplings for R^4 corrections in type II supergravity, correcting previous inconsistencies with string theory S-matrix results.

Findings

Corrected the R^4 supergravity corrections to match string S-matrix data.

Ensured T-duality invariance of the higher-order curvature couplings.

Derived a new Lagrangian density consistent with superstring theory.

Abstract

We observe that the replacement of the Riemann curvature with the generalized Riemann curvature into the corrections to the type II supergravity at order $\alpha'^3$ which are in terms of the contractions of four Riemann curvatures $R^4$, is not fully consistent with the S-matrix elements in the superstring theory. In particular, they produce non-zero S-matrix elements for odd number of B-field strengths which are not consistent with the string theory results. Using the consistency of the couplings with the linear T-duality as a guiding principle, we consider all T-duality invariant couplings and fix their coefficients by requiring them to be consistent with the S-matrix elements. The new Lagrangian density is then equivalent to the replacement of the generalized Riemann curvature into the expression $t_8t_8R^4$.