Tree-level $R^4$ correction from $O(d,d)$: NS-NS five-point terms

TL;DR

This paper derives a simplified form of the tree-level string effective action's R^4 correction, ensuring it respects the O(d,d) symmetry related to T-duality, by canceling out violating terms during dimensional reduction.

Contribution

It provides a complete, simplified expression for the quartic Riemann correction involving five NS-NS fields, maintaining O(d,d) symmetry.

Findings

Derived a consistent O(d,d)-invariant R^4 correction

Simplified the previously complex Lagrangian expressions

Ensured higher derivative terms preserve T-duality symmetry

Abstract

The tree-level string effective action reduced from $D$ to $D-d$ dimensions possesses a continuous $O(d,d)$ symmetry, closely related to T-duality. A necessary condition for a higher derivative correction to preserve this symmetry is that certain $O(d,d)$ violating terms which appear in the dimensional reduction have to cancel out. We use this idea to complete the quartic Riemann correction with all terms involving five NS-NS sector fields. The resulting Lagrangian is considerably simpler than expressions that have previously appeared in the literature.