On the Algebraic Theory of Soliton and Antisoliton Sectors

TL;DR

This paper explores the algebraic structure of soliton and antisoliton sectors in two-dimensional quantum field theories, analyzing their existence and classification within the Haag-Kastler framework.

Contribution

It introduces a classification of antisoliton sectors associated with solitons, highlighting conditions for their equivalence based on sector dimension.

Findings

Three different constructions for antisoliton sectors are identified.

Equivalence of these constructions depends on the finiteness of the sector's statistical dimension.

Provides a framework for understanding soliton-antisoliton duality in algebraic quantum field theory.

Abstract

We consider the properties of massive one particle states on a translation covariant Haag-Kastler net in Minkowski space. In two dimensional theories, these states can be interpreted as soliton states and we are interested in the existence of antisolitons. It is shown that for each soliton state there are three different possibilities for the construction of an antisoliton sector which are equivalent if the (statistical) dimension of the corresponding soliton sector is finite.