Lorentz violation, Two times physics and Strings

TL;DR

This paper explores a generalized relativistic particle model with Lorentz violation, revealing connections to two-time physics and string theory through alternative actions and symmetry considerations.

Contribution

It introduces an alternative action for a Lorentz-violating particle model and demonstrates its relation to two-time physics and string theory under certain symmetry limits.

Findings

Existence of a limit with enhanced local symmetries

Restoring Lorentz symmetry links to two-time physics

Restoring Poincaré symmetry yields relativistic string action

Abstract

We study a recently proposed generalization of the relativistic particle by Kosteleck\'y, that includes explicit Lorentz violation. We present an alternative action for this system and we show that this action can be interpreted as a particle in curved space with a metric that depends on the Lagrange multipliers. Furthermore, the following results are established for this model: (i) there exists a limit where this system has more local symmetries that the usual relativistic particle; (ii) in this limit if we restore the Lorentz symmetry we obtain a direct relationship with the two time physics; (iii) also we show that if we intent to restore the Poincar\'e symmetry we obtain the action of the relativistic bosonic string.