# $S$-dual amplitude and ${D}_{3}$-brane couplings

Babaei Velni, Komeil (Department of Physics, University of Guilan, P.O. Box 41335-1914, Rasht, Iran) ; Babaei-Aghbolagh, H (Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran)

15 March 2019

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 $SL\left(2,R\right)$ invariant form of the ${D}_{3}$-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 $SL\left(2,R\right)$ invariant structures, we find the action with derivative corrections at the level of more gauge fields.

Published in: Physical Review D 99 (2019)