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

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+πα′m2T2+12!(πα′m2T2)2+⋯ where m2=−1/(2α′)m2=−1/(2α′) is the mass of tachyon. This calculation fixes the coefficient of four-tachyon couplings without on-shell ambiguity.