Tree-level R⁴ correction from O(d, d): NS-NS five-point terms

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.