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 + θ2) where θ 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 I. The non-commutative chiral bosons are shown to correspond to a free fermion moving with a speed equal to c′ = c√1 - θ2 where c is the speed of light. Lorentz invariance remains intact if c is rescaled by c → c′. The dispersion relation for bosons and fermions, in this case, is given by w = c′ k|. © SISSA/ISAS 2004.