Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (I): Heterotic F⁶ Terms at Two Loops

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We study the two-loop F⁶ interactions in SO(32) heterotic superstring theory in D=10. By using the generalized Riemann identity we are able to determine the single-trace part of the effective action up to a few constants which are related to certain scattering amplitudes. This two-loop heterotic result is related by duality to Type I interactions at the tree level. However, it turns out to be completely different from any sort of non-Abelian generalization of Born-Infeld theory. We offer an explanation of this discrepancy.