Scaling limits of integrable quantum field theories

TL;DR

This paper investigates the short-distance scaling limits of integrable quantum field theories in two dimensions, demonstrating the existence of massless limits and their decomposition into chiral components with extended symmetries.

Contribution

It establishes the existence of massless scaling limit theories for integrable models and describes their decomposition into chiral components with extended symmetries.

Findings

Massless scaling limits exist for the models considered.

The limits decompose into twisted tensor products of chiral theories.

Interval-localized algebras are explicitly analyzed in examples.

Abstract

Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-local quantum fields generating these models, it is shown that massless scaling limit theories exist, and decompose into (twisted) tensor products of chiral, translation-dilation covariant field theories. On the subspace which is generated from the vacuum by the observables localized in finite light ray intervals, this symmetry can be extended to the M\"obius group. The structure of the interval-localized algebras in the chiral models is discussed in two explicit examples.