Non-abelian expansion of S-matrix elements and non-abelian tachyon DBI action

TL;DR

This paper applies a non-abelian expansion method to superstring S-matrix elements involving tachyons and gauge fields, confirming the non-abelian tachyon DBI action and fixing the tachyon potential coefficient.

Contribution

It demonstrates the agreement between the non-abelian expansion of superstring S-matrix elements and the tachyon DBI action, specifically fixing the tachyon potential coefficient.

Findings

Leading order terms match the non-abelian tachyon DBI action

Fixes the coefficient of T^4 term in the tachyon potential

Confirms the form of the tachyon potential in superstring theory

Abstract

We apply the prescription proposed in hep-th/0307197 for non-abelian expansion of S-matrix elements, to the S-matrix element of four tachyons and one gauge field in superstring theory. We show that the leading order terms of the expansion are in perfect agreement with the non-abelian generalization of the tachyon DBI action in which the tachyon potential is $V(T)=1+\pi\alpha' m^2T^2+\frac{1}{2!}(\pi\alpha' m^2T^2)^2+...$ where $m^2=-1/(2\alpha')$ is the mass of tachyon. This calculation fixes the coefficient of $T^4$ in the potential without on-shell ambiguity.