Chiral bosonization as a duality.

We demonstrate that the technique of abelian bosonization through duality transformations can be extended to gauging anomalous symmetries. The example of a Dirac fermion theory is first illustrated. This idea is then also applied to bosonize a chiral fermion by gauging its chiral phase symmetry. Two dimensional field theory has long proven to be a fruitful area of investigation. An interesting phenomenon in two dimensional field theory known to physicists for some time is bosonization [1]. It states the equality of the correlation function of some operators of two apparently different theories, one being a theory of a Dirac fermion and the other that of a scalar boson. Conventionally this equality is expressed in terms of bosonization rules [2][3]. A very elaborate framework for bosonization is smooth bosonization [4]. In this framework one deals with a family of theories containing both fermion and boson fields in which one may smoothly interpolate between a pure fermionic theory and a pure bosonic one. So considering only the bosonic and fermionic theories limits the discussion to a small sector of this larger framework. In a related point of view, C.P. Burgess and F. Quevedo [5] have shown how to systematically derive the bosonization rules in two dimensions as a particular case of a duality transformation [6]. The technique is, briefly stated, that first the phase symmetry of the fermion theory is gauged which adds a new gauge field Aμ to the theory. The corresponding field strength Fμν is then constrained so that it vanishes everywhere. This constraint can be incorporated through a Lagrange multiplier field φ. To obtain the bosonized action one fixes the gauge (∂ · A = 0) and integrates out the original fermion field as well as the new gauge field Aμ. One is then left with a bosonic action in terms of the