Solitons, Tau-functions and Hamiltonian Reduction for Non-Abelian Conformal Affine Toda Theories

TL;DR

This paper develops a class of non-abelian conformally invariant integrable models called G-CAT, constructs their soliton solutions using the Leznov-Saveliev method, and explores their mass spectrum upon symmetry breaking.

Contribution

It introduces the G-CAT models as non-abelian generalizations of conformal affine Toda theories, providing explicit soliton solutions and analyzing their mass spectrum.

Findings

G-CAT models are conformally invariant and possess soliton solutions.

Explicit construction of solutions via the Leznov-Saveliev method.

Analysis of soliton masses related to spontaneous symmetry breaking.

Abstract

We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra $\cgh$. The resulting reduced models, called {\em Generalized Non-Abelian Conformal Affine Toda (G-CAT)}, are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-abelian generalizations of the Conformal Affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the $\tau$-functions, which are defined for any integrable highest weight representation of $\cgh$, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized Affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed.