Solitons and Vertex Operators in Twisted Affine Toda Field Theories

TL;DR

This paper extends the study of soliton solutions and their masses from untwisted to twisted affine Toda field theories, revealing new solutions via algebraic foldings and vertex operator constructions.

Contribution

It introduces a folding procedure for affine Kac-Moody algebras to find new soliton solutions and explores their relation to twisted Coxeter elements and vertex operators.

Findings

New soliton solutions for twisted affine Toda theories

Explicit calculation of foldings related to automorphisms

Connection between vertex operators and soliton structures

Abstract

Affine Toda field theories in two dimensions constitute families of integrable, relativistically invariant field theories in correspondence with the affine Kac-Moody algebras. The particles which are the quantum excitations of the fields display interesting patterns in their masses and coupling and which have recently been shown to extend to the classical soliton solutions arising when the couplings are imaginary. Here these results are extended from the untwisted to the twisted algebras. The new soliton solutions and their masses are found by a folding procedure which can be applied to the affine Kac-Moody algebras themselves to provide new insights into their structures. The relevant foldings are related to inner automorphisms of the associated finite dimensional Lie group which are calculated explicitly and related to what is known as the twisted Coxeter element. The fact that the twisted affine Kac-Moody algebras possess vertex operator constructions emerges naturally and is relevant to the soliton solutions.