Chiral bosonization for non-commutative fields

TL;DR

This paper develops a model of chiral bosons in a non-commutative field space, introducing generalized bosonization rules, and explores the resulting conformal structure, Lorentz invariance, and dispersion relations.

Contribution

It presents a novel construction of non-commutative chiral bosons with new bosonization rules and analyzes their conformal and Lorentz-invariant properties.

Findings

Level of Kac-Moody algebra is (1+θ^2)

Chiral bosons correspond to free fermions with speed c' = c√(1+θ^2)

Lorentz invariance is preserved with a rescaled speed of light

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 $\omega = c^{\prime} | k|$.