On non-abelian generalisation of Born-Infeld action in string theory

TL;DR

This paper demonstrates that the non-abelian extension of the Born-Infeld action, relevant for string theory, can be expressed as a symmetrised trace, with implications for D-brane dynamics.

Contribution

It provides a non-abelian generalisation of the Born-Infeld action using the symmetrised trace, advancing understanding of open string effective actions.

Findings

The non-abelian Born-Infeld action is given by the symmetrised trace of the invariant.

Application to D-brane dynamics is discussed.

The approach clarifies the structure of the effective action for non-abelian gauge fields.

Abstract

We show that the part of the tree-level open string effective action for the non-abelian vector field which depends on the field strength but not on its covariant derivatives, is given by the symmetrised trace of the direct non-abelian generalisation of the Born-Infeld invariant. We discuss applications to D-brane dynamics.