Completing $R^4$ using $O(d,d)$

TL;DR

This paper derives the structure of quartic Riemann terms in the string effective action, ensuring $O(d,d)$ symmetry upon torus reduction, revealing a complex pattern of B-field couplings at higher orders.

Contribution

It introduces a method to determine B-field couplings in the $R^4$ term using $O(d,d)$ symmetry constraints, extending previous knowledge of string effective actions.

Findings

Derived B-field couplings up to fifth order in fields.

Revealed intricate structure of the $R^4$ terms under $O(d,d)$ symmetry.

Confirmed the form of the first $ ext{order }\alpha'^3$ correction in type II string theory.

Abstract

The tree-level string effective action is known to contain quartic Riemann terms with coefficient $\zeta(3)\alpha'^3$. In the case of the type II string this is the first $\alpha'$ correction. We use the requirement that the action reduced on a $d$-torus should have an $O(d,d)$ symmetry to find the B-field couplings up to fifth order in fields. The answer turns out to have a surprisingly intricate structure.