On the space of quantum fields in massive two-dimensional theories

TL;DR

This paper explores how the S-matrix in integrable massive 2D quantum field theories defines a structured space of fields, extending conformal levels and classifying primary fields across various models.

Contribution

It introduces a classification scheme for fields in integrable 2D QFTs based on the S-matrix, linking off-critical levels to conformal levels and unifying different models.

Findings

Fields decompose into subspaces labeled by charge, spin, and an integer k.

k is a non-negative integer for scalar fields, representing an off-critical extension of conformal level.

The classification applies to models like Z_n, sine-Gordon, and Ising with magnetic field.

Abstract

For a large class of integrable quantum field theories we show that the S-matrix determines a space of fields which decomposes into subspaces labeled, besides the charge and spin indices, by an integer k. For scalar fields k is non-negative and is naturally identified as an off-critical extension of the conformal level. To each particle we associate an operator acting in the space of fields whose eigenvectors are primary (k=0) fields of the massive theory. We discuss how the existing results for models as different as Z_n, sine-Gordon or Ising with magnetic field fit into this classification.