T-duality of O-plane action at order $ \alpha'^2$

TL;DR

This paper determines the NS-NS couplings in O-plane actions at order α'^2 by ensuring compatibility with nonlinear T-duality, revealing how dilaton couplings appear in the string frame.

Contribution

It introduces a method to derive O-plane NS-NS couplings at order α'^2 using T-duality constraints, clarifying the role of dilaton couplings in the string frame.

Findings

NS-NS couplings at order α'^2 are fully determined by T-duality.

Dilaton couplings appear only via a specific transformation of the Ricci tensor.

The approach ensures consistency of O-plane actions with T-duality symmetry.

Abstract

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 $\alpha'^2$. We find that the dilaton couplings appear in the string frame only via the transformation $\hat{R}_{\mu\nu}\rightarrow \hat{R}_{\mu\nu}+\nabla_{\mu}\nabla_{\nu}\phi$.