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

TL;DR

This paper derives the non-abelian open superstring effective action up to order 3, revealing a unique solution at 2 and a one-parameter family at 3, emphasizing the importance of derivative terms.

Contribution

It extends the non-abelian Born-Infeld action to order 3, providing a detailed analysis of deformations and the role of derivative terms, building on previous methods.

Findings

Unique solution at order 2 after field redefinitions

Discovery of a one-parameter family of deformations at order 3

Derivative terms are crucial for the deformation structure

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.