Modular Wedge Localization and the d=1+1 Formfactor Program

TL;DR

This paper advances the understanding of modular localization in 1+1 dimensions, focusing on wedge-localized algebras, formfactor programs, and their connections to algebraic structures like Zamolodchikov-Faddeev and implications for anyons.

Contribution

It introduces semilocal generators of wedge-localized algebras without vacuum polarization and explores their relation to formfactors and algebraic structures in 1+1 dimensions.

Findings

Established the existence of FWG-operators related to Zamolodchikov-Faddeev algebra

Linked KMS conditions with cyclicity equations for formfactors

Proposed new ideas on free anyons and plektons in 2+1 dimensions

Abstract

In this paper I continue the study of the new framework of modular localization and its constructive use in the nonperturbative d=1+1 Karowski-Weisz-Smirnov formfactor program. Particular attention is focussed on the existence of semilocal generators of the wedge-localized algebra without vauum polarization (FWG-operators) which are closely related to objects fulfilling the Zamolodchikov-Faddeev algebraic structure. They generate a ``thermal Hilbert space'' and allow to understand the equivalence of the KMS conditions with the so-called cyclicity equation for formfactors which was known to be closely related to crossing symmetry properties. The modular setting gives rise to interesting new ideas on ``free'' d=2+1 anyons and plektons.