Massive Integrable Soliton Theories

TL;DR

This paper explores massive integrable 1+1 dimensional field theories with non-abelian symmetry, generalizing sine-Gordon models, and discusses their quantization, soliton charges, and relation to conformal field theories.

Contribution

It introduces a class of massive integrable theories with non-abelian fields, extending known models and analyzing their quantization and soliton properties.

Findings

Coupling constant is quantized in these theories.

Solitons carry non-abelian charges.

Theories are related to perturbations of coset conformal field theories.

Abstract

Massive integrable field theories in $1+1$ dimensions are defined at the Lagrangian level, whose classical equations of motion are related to the ``non-abelian'' Toda field equations. They can be thought of as generalizations of the sine-Gordon and complex sine-Gordon theories. The fields of the theories take values in a non-abelian Lie group and it is argued that the coupling constant is quantized, unlike the situation in the sine-Gordon theory, which is a special case since its field takes values in an abelian group. It is further shown that these theories correspond to perturbations of certain coset conformal field theories. The solitons in the theories will, in general, carry non-abelian charges.