Bosonization, soliton-particle duality and Mandelstam-Halpern operators

TL;DR

This paper develops a bosonization framework for the generalized massive Thirring model with multiple fermion species, establishing a duality with a generalized sine-Gordon model and revealing a confinement mechanism through soliton-fermion mapping.

Contribution

It introduces generalized Mandelstam-Halpern operators and bosonization rules for multi-species models, extending Abelian bosonization to non-Abelian contexts with explicit fermion-soliton duality.

Findings

Constructed generalized Mandelstam-Halpern soliton operators.

Established fermion-boson mapping via bosonization rules.

Demonstrated confinement mechanism leading to massive fermions.

Abstract

The generalized massive Thirring model (GMT) with $N_{f}$[=number of positive roots of $su(n)$] 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 $N_{f}$ interacting soliton species. The generalized Mandelstam-Halpern 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(n) 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 $su(3)$ and $su(4)$ cases are discussed in detail.