Higher Grading Conformal Affine Toda Teory and (Generalized) Sine-Gordon/Massive Thirring Duality

TL;DR

This paper explores higher grading integrable conformal affine Toda systems, revealing their off-critical behavior, dualities with sine-Gordon and massive Thirring models, and detailed analysis for specific affine Lie algebras.

Contribution

It introduces a new real, local Lagrangian for off-critical models, demonstrating dualities and soliton sector descriptions in affine Toda theories.

Findings

Off-critical models exhibit Noether-topological current equivalence.

Derived a real, local Lagrangian describing soliton sectors.

Uncovered dual phases related to generalized sine-Gordon and Thirring models.

Abstract

Some properties of the higher grading integrable generalizations of the conformal affine Toda systems are studied. The fields associated to the non-zero grade generators are Dirac spinors. The effective action is written in terms of the Wess-Zumino-Novikov-Witten (WZNW) action associated to an affine Lie algebra, and an off-critical theory is obtained as the result of the spontaneous breakdown of the conformal symmetry. Moreover, the off-critical theory presents a remarkable equivalence between the Noether and topological currents of the model. Related to the off-critical model we define a real and local Lagrangian provided some reality conditions are imposed on the fields of the model. This real action model is expected to describe the soliton sector of the original model, and turns out to be the master action from which we uncover the weak-strong phases described by (generalized) massive Thirring and sine-Gordon type models, respectively. The case of any (untwisted) affine Lie algebra furnished with the principal gradation is studied in some detail. The example of $\hat{sl}(n) (n=2,3)$ is presented explicitly.