The non-abelian open superstring effective action through order $α'{}^3$

Using the method developed in {\tt hep-th/0103015}, we determine the non-abelian Born-Infeld action through ${\cal O}(α'{}^3)$. 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 ${\cal O}(α'{}^2)$, a unique, modulo field redefinitions, solution emerges. At ${\cal O}(α'{}^3)$ 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.

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