Realization of Cohen-Glashow Very Special Relativity on Noncommutative Space-Time

We show that the Cohen-Glashow very special relativity (VSR) theory [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. 97, 021601 (2006)] can be realized as the part of the Poincaré symmetry preserved on a noncommutative Moyal plane with lightlike noncommutativity. Moreover, we show that the three subgroups relevant to VSR can also be realized in the noncommutative space-time setting. For all of these three cases, the noncommutativity parameter ${\theta }^{\mu \nu }$ should be lightlike (${\theta }^{\mu \nu }{\theta }_{\mu \nu }=0$). We discuss some physical implications of this realization of the Cohen-Glashow VSR.