Bosonization and generalized Mandelstam soliton operators

TL;DR

This paper demonstrates the bosonization of the three-species massive Thirring model into a generalized sine-Gordon model, establishing a fermion-soliton duality and revealing a confinement mechanism through a semi-classical limit.

Contribution

It introduces generalized Mandelstam soliton operators and extends the bosonization framework to a three-species model with higher rank Lie algebra considerations.

Findings

Fermion species are mapped to solitons via generalized bosonization rules.

The semi-classical limit recovers the SU(3) affine Toda model coupled to matter fields.

A confinement mechanism is suggested by the disappearance of certain spinor fields from the physical spectrum.

Abstract

The generalized massive Thirring model (GMT) with three fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized sine-Gordon model (GSG) with three interacting soliton species. The generalized Mandelstam soliton operators are constructed and the fermion-boson mapping is established through a set of generalized bosonization rules in a quotient positive definite Hilbert space of states. Each fermion species is mapped to its corresponding soliton in the spirit of particle/soliton duality of Abelian bosonization. In the semi-classical limit one recovers the so-called SU(3) affine Toda model coupled to matter fields (ATM) from which the classical GSG and GMT models were recently derived in the literature. The intermediate ATM like effective action possesses some spinors resembling the higher grading fields of the ATM theory which have non-zero chirality. These fields are shown to disappear from the physical spectrum, thus providing a bag model like confinement mechanism and leading to the appearance of the massive fermions (solitons). The ordinary MT/SG duality turns out to be related to each SU(2) sub-group. The higher rank Lie algebra extension is also discussed.