The non-abelian Born-Infeld action through order $\alpha'{}^3$

Abstract

Using the method developed in {\\tt hep-th/0103015}, we determine the non-abelian Born-Infeld action through ${\\cal O}(\\alpha'{}^3)$. We start from solutions to a Yang-Mills theory which define a stable holomorphic vector bundle. Subsequently we investigate its deformation away from this limit. Through $ {\\cal O}(\\alpha'{}^2)$, a unique, modulo field redefinitions, solution emerges. At $ {\\cal O}(\\alpha'{}^3)$ we find a one-parameter family of allowed deformations. The presence of derivative terms turns out to be essential. Finally, we present a detailed comparison of our results to existing, partial results.