Chiral bosonization for non-commutative fields

Abstract

A model of chiral bosons on a non-commutative field space is constructed and new generalized bosonization (fermionization) rules for these fields are given. The conformal structure of the theory is characterized by a level of the Kac-Moody algebra equal to $(1+{\theta }^2)$ where $\theta$ is the non-commutativity parameter and chiral bosons living in a non-commutative fields space are described by a rational conformal field theory with the central charge of the Virasoro algebra equal to 1. The non-commutative chiral bosons are shown to correspond to a free fermion moving with a speed equal to $c^{\prime }=c\sqrt{1+{\theta }^2}$ where $c$ is the speed of light. Lorentz invariance remains intact if $c$ is rescaled by $c\to c^{\prime }$. The dispersion relation for bosons and fermions, in this case, is given by $\omega =c^{\prime }|k|$.

16 pages, JHEP style, version published in JHEP