On D-brane action at order $ \alpha'^2$

TL;DR

This paper determines the precise form of D-brane actions at order α'^2 in type II superstring theories by ensuring compatibility with dualities and S-matrix calculations, revealing new curvature couplings and dilaton interactions.

Contribution

It systematically derives all relevant world volume couplings at order α'^2, highlighting the role of second fundamental form squares and dilaton contributions in string frame.

Findings

Second fundamental form squares appear only in world volume curvatures.

Dilaton enters the string frame action through a specific curvature transformation.

The derived couplings are consistent with duality symmetries and S-matrix results.

Abstract

We use compatibility of D-brane action with linear T-duality, S-duality and with S-matrix elements as guiding principles to find all world volume couplings of one massless closed and two open strings at order $\alpha'^2$ in type II superstring theories. In particular, we find that the squares of second fundamental form appear only in world volume curvatures, and confirm the observation that dilaton appears in string frame action via the transformation $\hat{R}_{\mu\nu}\rightarrow \hat{R}_{\mu\nu}+\nabla_{\mu}\nabla_{\nu}\Phi$.