On the Lorentz symmetry of the noncommutative chiral bosons

TL;DR

This paper investigates Lorentz symmetry in noncommutative chiral boson theories, revealing that while the Lorentz group structure is preserved, the velocity of light can be scaled or maintained depending on the model, with implications for preferred-frame effects.

Contribution

It generalizes noncommutative chiral boson models to larger groups and analyzes Lorentz violation, including velocity scaling and birefringence effects, within this framework.

Findings

Velocity of light is scaled by a deformation parameter in most models.

A subset of models maintains the original velocity despite deformation.

Birefringence effects suggest a preferred frame in the extended Standard Model.

Abstract

We study issues of Lorentz violation symmetry in the context of the recently proposed theory of noncommutative fields \cite{CCGM}, using the soldering formalism. To this end a noncommutative chiral-boson with a deformed algebra \cite{DGMJ}, used to study these notions in D=2, is properly generalized. We verify, also for this larger group of theories that, although the structure of the Lorentz group is preserved, the velocity of light is scaled by a function of the deformation parameter, as recently claimed. However, we found a sub-set of models where the velocity of propagation is maintained in spite of the presence of the deformed algebra. Effects of a preferred-frame of reference manifest by the presence of birefringence were also studied in the chiral boson framework leading to the scalar sector of the extended Standard Model recently proposed.