S -dual amplitude and D3 -brane couplings

Komeil Babaei Velni,H Babaei-Aghbolagh

doi:10.1103/physrevd.99.066007

Komeil Babaei Velni, H Babaei-Aghbolagh

Open Access

https://doi.org/10.1103/physrevd.99.066007

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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

Highlights

We find a SLð2; RÞ 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 SLð2; RÞ invariant structures, we find the action with derivative corrections at the level of more gauge fields
It has been shown that the consistency of an electrodynamics theory under the duality transformation can be expressed as a requirement in which the Lagrangian must transform under duality in a particular way, defined by the Noether-Gaillard-Zumino (NGZ) identity [1]

Summary

INTRODUCTION

It has been shown that the consistency of an electrodynamics theory under the duality transformation can be expressed as a requirement in which the Lagrangian must transform under duality in a particular way, defined by the Noether-Gaillard-Zumino (NGZ) identity [1]. Leading order of D3-brane effective action in superstring theory contains four gauge fields and four derivatives [15,19,23]: Lð∂FÞ4 1⁄4 e−2φ. This action satisfies the NGZ identity, and is consistent with electromagnetic self-duality [19]. Considering the propagator and vertex VbðA; F2; Φ3; Φ4Þ in (16) and using the fourth order in the expansion of D-brane action to find the vertex operator VaðB1; AÞ 1⁄4 e−φ0 k1 · Ba1, one finds the pole part of B-field amplitude as following: Apole ðB1. We consider all contractions of the SLð2; RÞ invariant structure F TMB with four, two, and zero momenta, as follows: ðF

C MÞ: ð21Þ

S-DUAL AMPLITUDE OF THREE GAUGE FIELDS AND ONE TWO-FORM

S-DUAL EFFECTIVE ACTION WITH FOUR DERIVATIVE CORRECTIONS