Higher derivative corrections to O-plane actions: NS-NS sector

We classify all possible two- and four-derivative couplings of bulk NS-NS sector fields to a single Op-plane which are compatible with diffeomorphism invariance and B-field gauge invariance. This is applicable to type IIA or IIB superstrings or to the bosonic string. We then consider this general action in various classes of backgrounds that admit a U(1) isometry and determine the constraints on the couplings from consistency with T-duality. We show that this consistency requires the two-derivative action to vanish, and the entire non-linear four-derivative action is fixed up to one overall constant which can be determined by comparison with a two-point scattering amplitude. The resulting action is consistent with all previously computed couplings.