Crossing and Antisolitons in Affine Toda Theories

TL;DR

This paper explores the properties of solitons and antisolitons in affine Toda theories, revealing a classical crossing symmetry linked to affine Kac-Moody groups that simplifies soliton solution calculations.

Contribution

It demonstrates the equivalence of two antisoliton realizations through a novel identity in affine Kac-Moody groups, connecting classical solutions to S-matrix crossing symmetry.

Findings

Identifies a classical crossing property in affine Toda solitons.

Shows the equivalence of two antisoliton realization methods.

Simplifies explicit soliton solution calculations.

Abstract

Affine Toda theory is a relativistic integrable theory in two dimensions possessing solutions describing a number of different species of solitons when the coupling is chosen to be imaginary. These nevertheless carry real energy and momentum. To each species of soliton there has to correspond an antisoliton species. There are two different ways of realising the antisoliton whose equivalence is shown to follow from a surprising identity satisfied within the underlying affine Kac-Moody group. This is the classical analogue of the crossing property of analytic S-matrix theory. Since a complex parameter related to the coordinate of the soliton is inverted, this identity implies a sort of modular transformation property of the soliton solution. The results simplify calculations of explicit soliton solutions.