Towards a supersymmetric non-abelian Born-Infeld theory

TL;DR

This paper develops a method to construct a non-abelian extension of the Born-Infeld action using kappa-symmetry constraints, calculating bosonic and fermionic terms up to specific orders, revealing deviations from the symmetric trace prescription.

Contribution

It introduces an iterative procedure for non-abelian Born-Infeld action construction, incorporating kappa-symmetry to determine higher-order terms.

Findings

Bosonic terms calculated up to quartic order in field strength.

Fermionic bilinear terms computed up to cubic order.

Fermionic terms deviate from the symmetric trace prescription.

Abstract

We define an iterative procedure to obtain a non-abelian generalization of the Born-Infeld action. This construction is made possible by the use of the severe restrictions imposed by kappa-symmetry. We have calculated all bosonic terms in the action up to terms quartic in the Yang-Mills field strength and all fermion bilinear terms up to terms cubic in the field strength. Already at this order the fermionic terms do not satisfy the symmetric trace-prescription.