Supersymmetric non-abelian Born-Infeld revisited

TL;DR

This work determines the non-abelian open-string effective action through order ${ ilde\alpha}'^2$ by computing four-point disc amplitudes and organizing the result via field redefinitions into a symmetric-trace form. It shows that, including fermions, the action matches a modified symmetric-trace prescription through this order and is consistent with linear and nonlinear supersymmetry analyses, while κ-symmetry cannot be extended to cubic orders in the Born–Infeld curvature. The results reconcile string amplitudes with field-theory D-brane effective actions and clarify the limitations of non-abelian κ-symmetry, highlighting the role of field redefinitions in implementing the symmetric-trace structure. They also align with Goteborg’s findings on linear supersymmetry and clarify that κ-symmetry, if present, may require a different formulation beyond the BdRS approach. The analysis cautions against assuming the symmetric-trace prescription at higher orders and motivates further exploration of alternative κ-invariant frameworks or nonlinear realizations of supersymmetry.

Abstract

We determine the non-abelian Born-Infeld action, including fermions, as it results from the four-point tree-level open superstring scattering amplitudes at order alpha'^2. We find that, after an appropriate field redefinition all terms at this order can be written as a symmetrised trace. We confront this action with the results that follow from kappa-symmetry and conclude that the recently proposed non-abelian kappa-symmetry cannot be extended to cubic orders in the Born-Infeld curvature.

Figures (2)

• Figure 1: 2 boson / 2 fermion scattering amplitude
• Figure 2: The six different cyclic orderings