Completing R4 using O(d, d)

Abstract

The tree-level string effective action is known to contain quartic Riemann terms with coefficient ζ(3)α′3. In the case of the type II string this is the first α′ 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.