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 $\hat{R}_{μν}\rightarrow \hat{R}_{μν}+\nabla_μ\nabla_νϕ$.

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