Invariant length scale in relativistic kinematics - Lessons from Dirichlet branes

TL;DR

This paper reveals a hidden invariance in Dirac-Born-Infeld theory that introduces a fundamental invariant length scale into relativistic kinematics, impacting observer acceleration bounds and challenging traditional views on space-time and Lorentz symmetry.

Contribution

It uncovers a hidden O(1,p) x O(1,p) gauge symmetry in Dirac-Born-Infeld theory that encodes an invariant length scale, with implications for gravity and string phenomenology.

Findings

Observer accelerations are bounded from above.

A fundamental length scale can be integrated into relativistic kinematics.

Space-time can remain smooth and Lorentz-invariant despite the invariant scale.

Abstract

We show that Dirac-Born-Infeld theory possesses a hidden invariance that enhances the local O(1,p) Lorentz symmetry on a Dirichlet p-brane to an O(1,p) x O(1,p) gauge group, encoding both an invariant velocity and acceleration (or length) scale. This enlarged gauge group predicts consequences for the kinematics of observers on Dirichlet branes, with admissible accelerations being bounded from above. An important lesson beyond string theory is that a fundamental length scale can be implemented into the kinematics of general relativity, whilst preserving both space-time as a smooth manifold and local Lorentz symmetry, contrary to common belief. We point out consequences for string phenomenology, classical gravity and atomic physics.