Dirac-Born-Infeld action from spontaneous breakdown of Lorentz symmetry in brane-world scenarios

TL;DR

This paper demonstrates that the Dirac-Born-Infeld action naturally arises from the spontaneous breakdown of Lorentz symmetry in brane-world models, showing its invariance under non-linear symmetry realizations and identifying it as the most general form under certain conditions.

Contribution

It uncovers the specific non-linear realization of Lorentz symmetry breaking in brane scenarios and proves the Dirac-Born-Infeld action's invariance and uniqueness in this context.

Findings

Dirac-Born-Infeld action is invariant under non-linear Lorentz transformations.

The most general invariant action reduces to a combination of DBI terms with different scales.

String theory results are recovered assuming a single length scale dependence.

Abstract

In whatever Lorentz invariant theory, the presence of extended d-dimensional objects inside a higher dimensional bulk space-time, like for instance D-branes in string theories, induces a spontaneous breakdown of the Poincare' invariance of the bulk; however the effective action describing these extended objects should still respect this larger invariance through a non-linear realization of the full symmetry. Here the specific form of such a realization in presence of an electromagnetic field is uncovered. The Dirac-Born-Infeld type action for a D-brane turns out to be invariant under such transformations. Conversely it is explicitly demonstrated in some simple cases that the most general invariant action, as long as derivatives of the field strength (and second derivatives of the scalars) can be neglected, is a linear combination of terms of the Dirac-Born-Infeld type with different scale parameters. The string result is obtained if one further assumes that the theory depends upon a single length scale.