# S-dual Amplitude and D3-Brane Couplings

## TL;DR

This paper explores S-duality in type IIB string theory, deriving S-matrix elements and D3-brane effective actions that respect SL(2, R) invariance, including derivative corrections for multiple gauge fields.

## Contribution

It introduces a method to impose S-duality on tree-level amplitudes and derives an SL(2, R) invariant D3-brane effective action with derivative corrections.

## Key findings

- S-matrix elements consistent with S-duality
- SL(2, R) invariant D3-brane action with derivative corrections
- Extension to multiple gauge fields with derivative terms

## Abstract

Recently, it has been observed that the IIB scattering amplitudes are compatible with the standard rules of S-duality. Inspired by this observation, we will find the tree-level S-matrix elements of one Ramond-Ramond and three open strings by imposing this symmetry on the tree-level S-matrix elements of one Kalb-Ramond and three open strings. We also find a SL(2, R) invariant form of the D3-brane effective action containing four gauge fields with derivative corrections that was derived from one-loop level four-point amplitude. Using the expansion of the nonlinear SL(2, R) invariant structures, we find the action with derivative corrections at the level of more gauge fields