On Soliton Automorphisms in Massive and Conformal Theories

TL;DR

This paper establishes a unified framework for understanding soliton automorphisms in 1+1 dimensional massive and conformal quantum field theories, providing conditions for their existence and covariance.

Contribution

It offers a necessary and sufficient condition for the existence and Poincare' covariance of soliton automorphisms applicable to a broad class of theories, including conformal and Fock property models.

Findings

Unified treatment of soliton automorphisms in massive and conformal theories.

Applicable to models with local Fock property and holomorphic conformal field theories.

Lays groundwork for analyzing superselection sectors in orbifold theories.

Abstract

For massive and conformal quantum field theories in 1+1 dimensions with a global gauge group we consider soliton automorphisms, viz. automorphisms of the quasilocal algebra which act like two different global symmetry transformations on the left and right spacelike complements of a bounded region. We give a unified treatment by providing a necessary and sufficient condition for the existence and Poincare' covariance of soliton automorphisms which is applicable to a large class of theories. In particular, our construction applies to the QFT models with the local Fock property -- in which case the latter property is the only input from constructive QFT we need -- and to holomorphic conformal field theories. In conformal QFT soliton representations appear as twisted sectors, and in a subsequent paper our results will be used to give a rigorous analysis of the superselection structure of orbifolds of holomorphic theories.