Higher particle form factors of branch point twist fields in integrable quantum field theories

TL;DR

This paper calculates higher particle form factors of branch point twist fields in integrable quantum field theories, linking their correlation functions to entanglement entropy and analyzing their behavior across different energy scales.

Contribution

It provides analytic expressions for higher particle form factors of twist fields and explores their consistency and relation to conformal dimensions in integrable models.

Findings

Form factors are not unique, requiring multiple techniques for identification.

The models exhibit staircase patterns in physical quantities as energy varies.

Renormalization group flows approach multiple critical points before reaching the UV fixed point.

Abstract

In this paper we compute higher particle form factors of branch point twist fields. These fields were first described in the context of massive 1+1-dimensional integrable quantum field theories and their correlation functions are related to the bi-partite entanglement entropy. We find analytic expressions for some form factors and check those expressions for consistency, mainly by evaluating the conformal dimension of the corresponding twist field in the underlying conformal field theory. We find that solutions to the form factor equations are not unique so that various techniques need to be used to identify those corresponding to the branch point twist field we are interested in. The models for which we carry out our study are characterized by staircase patterns of various physical quantities as functions of the energy scale. As the latter is varied, the beta-function associated to these theories comes close to vanishing at several points between the deep infrared and deep ultraviolet regimes. In other words, renormalisation group flows approach the vicinity of various critical points before ultimately reaching the ultraviolet fixed point. This feature provides an optimal way of checking the consistency of higher particle form factor solutions, as the changes on the conformal dimension of the twist field at various energy scales can only be accounted for by considering higher particle form factor contributions to the expansion of certain correlation functions.