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 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.

Automated summary

The tree-level string effective action contains quartic Riemann terms with coefficient zeta(3)alpha'(3). This is the first alpha' correction in the case of the type II string. By using the requirement of O(d, d) symmetry for the action reduced on a d-torus, we have determined the B-field couplings up to fifth order in fields. The result reveals a surprisingly intricate structure.