Space-time transformations of the Born-Infeld gauge field of a D-brane

TL;DR

This paper explores how the transformation properties of the Born-Infeld gauge field on a D-brane can be derived from gauge fixing and reparametrization, clarifying their relation to space-time symmetries.

Contribution

It demonstrates that the gauge field's transformation properties follow directly from gauge fixing and reparametrization, linking them to space-time Lorentz transformations.

Findings

Transformation properties derived from gauge fixing

Connection between gauge transformations and Lorentz symmetry

Clarification of the gauge field's space-time behavior

Abstract

Recently Gliozzi has shown that, under certain conditions, it is possible to derive the Dirac-Born-Infeld action for an abelian gauge field of a D-brane. Also, the action turns out to be invariant with respect to a non-linear realization of the full Poincar\'e group. A crucial role is played by the transformation properties of the gauge field under the non-linear realization. The aim of this note is to point out that these transformation properties are derived directly from the gauge fixing of the diffeomorphisms of the brane and the necessary compensating reparametrization when one performs a Lorentz transformation.