Completing R4 using O(d, d)

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