The open superstring 5-point amplitude revisited

TL;DR

This work computes the complete open-string tree-level five-gluon amplitude and its expansion up to $\mathcal{O}({\alpha'}^3)$, providing a direct test of higher-derivative corrections to non-abelian gauge theory. By expressing the five-point result as $A(1,2,3,4,5)=A^{(0)}+A^{(2)}{\alpha'}^{2}+A^{(3)}{\alpha'}^{3}+\mathcal{O}({\alpha'}^{4})$, the authors confirm that $A^{(0)}$ reproduces Yang–Mills, while $A^{(2)}$ and $A^{(3)}$ encode stringy corrections governed by a hierarchy of kinematic factors. Their analysis shows that the ${\cal O}({\alpha'}^3)$ terms in the effective lagrangian agree completely with Koerber–Sevrin’s ${\cal L}_{(3)}$ (including the $F^5$ sector), resolving previous controversies about non-equivalent proposals. The results reinforce the link between string corrections and the non-abelian Born–Infeld action and demonstrate a robust procedure for extracting higher-order effective actions from on-shell amplitudes.

Abstract

We derive the complete five-gluon scattering amplitude at tree level, within the context of Open Superstring theory. We find the general expression in terms of kinematic factors, and also find its complete expansion up to ${\cal O}({α'}^3)$ terms. We use our scattering amplitude to test three non-equivalent ${\cal O}({α'}^3)$ effective lagrangians that have recently been matter of some controversy.