A covariant approach to gauged 2D self-dual fields

Abstract

It is shown that the chiral boson model of Floreanini and Jackiw (FJ) and of MClain, Wu and Yu (MWY) are two different representations of the same chiral theory, each displaying different aspects of the bosonic representation for chiral fields: while in the FJ side the spectrum is quite evident from the equations of motion, it lacks manifest covariance making the coupling to external fields particularly difficult. On the MWY side, a symmetry hidden in the FJ version is apparent due to the presence of infinite scalar Wess-Zumino fields that carry the chiral representation in this side of the problem. On the other hand the evidence of physical spectrum is lost. In this work we show how to go from one representation to the other and find that the FJ chiral field is a collective field built by a linear combination of all MWY scalar fields. Using then the manifest covariance of the MWY representation we study the problem of coupling bosonic chiral fields to a background gauge field.