An Arena for Model Building in the Cohen-Glashow Very Special Relativity

TL;DR

This paper explores how noncommutative Moyal space-time can serve as a mathematical foundation for VSR-invariant quantum field theories, potentially guiding the development of VSR-based particle physics models with experimental implications.

Contribution

It demonstrates that light-like noncommutative space-time provides a consistent framework for VSR-invariant theories, introducing a deformation parameter related to the noncommutativity scale.

Findings

VSR-invariant theories can be formulated on noncommutative Moyal space-time.

The noncommutativity scale _{NC} is constrained to be above 1-10 TeV.

The framework sets the stage for constructing VSR-based particle physics models.

Abstract

The Cohen-Glashow Very Special Relativity (VSR) algebra [arXiv:hep-ph/0601236] is defined as the part of the Lorentz algebra which upon addition of CP or T invariance enhances to the full Lorentz group, plus the space-time translations. We show that noncommutative space-time, in particular noncommutative Moyal plane, with light-like noncommutativity provides a robust mathematical setting for quantum field theories which are VSR invariant and hence set the stage for building VSR invariant particle physics models. In our setting the VSR invariant theories are specified with a single deformation parameter, the noncommutativity scale \Lambda_{NC}. Preliminary analysis with the available data leads to \Lambda_{NC}\gtrsim 1-10 TeV. This note is prepared for the Proceedings of the G27 Mathematical Physics Conference, Yerevan 2008, and is based on arXiv:0806.3699[hep-th].