Noether and topological currents equivalence and soliton/particle correspondence in affine $sl(2)^{(1)}$ Toda theory coupled to matter

TL;DR

This paper explores the affine $sl(2)^{(1)}$ Toda theory coupled to matter, demonstrating the equivalence of Noether and topological currents, and establishing a soliton/particle correspondence in the off-critical regime.

Contribution

It introduces an effective off-critical affine Toda model coupled to matter, showing it retains key properties like soliton solutions and current equivalences from the conformal model.

Findings

The ATM model inherits soliton solutions from the CATM model.

The Noether and topological currents are equivalent in the ATM.

The classical solitonic spectrum of the ATM model is characterized.

Abstract

A submodel of the so-called conformal affine Toda model coupled to the matter field (CATM) is defined such that its real Lagrangian has a positive-definite kinetic term for the Toda field and a usual kinetic term for the (Dirac) spinor field. After spontaneously broken the conformal symmetry by means of BRST analysis, we end up with an effective theory, the off-critical affine Toda model coupled to the matter (ATM). It is shown that the ATM model inherits the remarkable properties of the general CATM model such as the soliton solutions, the particle/soliton correspondence and the equivacence between the Noether and topological currents. The classical solitonic spectrum of the ATM model is also discussed.