Disorder Operators, Quantum Doubles, and Haag Duality in 1+1 Dimensions

TL;DR

This paper explores how Drinfeld's quantum double D(G) acts as a hidden symmetry in various massive 1+1 dimensional quantum field theories with compact symmetry groups, independent of integrability.

Contribution

It establishes the role of quantum doubles as spontaneously broken hidden symmetries in massive quantum field theories without relying on integrability.

Findings

Quantum double D(G) identified as a hidden symmetry

Applicability to a broad class of massive models

Independence from exact integrability assumptions

Abstract

We demonstrate the role of Drinfeld's quantum double D(G) as a spontaneously broken hidden symmetry in a large class of massive quantum field theories in 1+1 dimensions with compact symmetry group G. Our considerations are independent of exact integrability. The main technical ingredient is an assumption concerning the statistical independence of fields localized in spacelike separated regions which should hold in all reasonable massive models. The present note is an abridged version of hep-th/9606175.