Generalized sine-Gordon/massive Thirring models and soliton/particle correspondences

TL;DR

This paper explores a generalized affine Toda model linked to sine-Gordon and Thirring models, revealing soliton/particle dualities and strong/weak coupling phases through a constrained Lagrangian framework.

Contribution

It introduces a parent Lagrangian for the generalized sine-Gordon and Thirring models, establishing dualities and soliton/particle correspondences in an affine Toda context.

Findings

Derived relationships between GMT spinor bilinears and GSG fields.

Identified strong and weak coupling phases.

Outlined generalizations for the $sl(n)^{(1)}$ case.

Abstract

We consider a real Lagrangian off-critical submodel describing the soliton sector of the so-called conformal affine $sl(3)^{(1)}$ Toda model coupled to matter fields (CATM). The theory is treated as a constrained system in the context of Faddeev-Jackiw and the symplectic schemes. We exhibit the parent Lagrangian nature of the model from which generalizations of the sine-Gordon (GSG) or the massive Thirring (GMT) models are derivable. The dual description of the model is further emphasized by providing the relationships between bilinears of GMT spinors and relevant expressions of the GSG fields. In this way we exhibit the strong/weak coupling phases and the (generalized) soliton/particle correspondences of the model. The $sl(n)^{(1)}$ case is also outlined.