S-duality of D-brane action at order $O(\alpha'^2)$

TL;DR

This paper explores the S-duality of D-brane actions at order $O(\alpha'^2)$, deriving nonlinear RR couplings and confirming quadratic RR couplings through scattering amplitudes, while expressing results in an $SL(2,Z)$ invariant form.

Contribution

It introduces the nonlinear RR couplings at order $O(\alpha'^2)$ consistent with S-duality and confirms quadratic RR couplings via scattering amplitudes, extending previous curvature correction analyses.

Findings

Derived nonlinear RR couplings at order $O(\alpha'^2)$

Confirmed quadratic RR couplings through disk-level scattering amplitudes

Expressed results in $SL(2,Z)$ invariant form

Abstract

Using the compatibility of the DBI and the Chern-Simons actions with the T-duality transformations, the curvature corrections to these actions have been recently extended to include the quadratic B-field couplings at order $O(\alpha'^2)$. In this paper, we use the compatibility of the couplings on D$_3$-brane with the S-duality to find the nonlinear RR couplings at order $O(\alpha'^2)$. We confirm the quadratic RR couplings in the DBI part with the disk-level scattering amplitude. Using the regularized non-holomorphic Eisenstein series $E_1$, we then write the results in $SL(2,Z)$ invariant form.