T-duality of O-plane action at order α′2

We use compatibility of O-plane action with nonlinear T-duality as a guiding principle to find all NS–NS couplings in the O-plane action at order α′2. We find that the dilaton couplings appear in the string frame only via the transformation Rˆμν→Rˆμν+∇μ∇νϕ.