Form factors of composite branch-point twist operators in the sinh-Gordon model on a multi-sheeted Riemann surface: semiclassical limit

TL;DR

This paper develops a semiclassical method to compute form factors of composite branch-point twist operators in the sinh-Gordon model on multi-sheeted Riemann surfaces, aiding entanglement entropy calculations.

Contribution

It introduces a novel semiclassical approach to determine form factors of composite twist operators in the sinh-Gordon model, linking them to basic fields.

Findings

Form factors of CTOs can be computed semiclassically.

The method simplifies the identification of operators in integrable models.

Results facilitate entanglement entropy calculations in quantum field theory.

Abstract

Quantum sinh-Gordon model in 1+1 dimensions is one of the simplest and best-studied massive integrable relativistic quantum field theories. We consider this theory on a multi-sheeted Riemann surfaces with a flat metric, which can be seen as a pile of planes connected to each other along cut lines. The cut lines end at branch points, which are represented by a twist operator ${\cal T}_n.$ Operators of such kind are interesting in the framework of the problem of computing von Neumann and Renyi entanglement entropies in the original model on the plane. The composite branch-point twist operators (CTO) are a natural generalization of the twist operators, obtained by placing a local operator to a branch point by means of a certain limiting procedure. Correlation function in quantum field theory can be, in principle, found by means of the spectral decomposition. It allows one to express them in terms of form factors of local operators, i.e. their matrix elements in the basis of stationary states. In integrable models complete sets of exact form factors of all operators can be found exactly as solutions of a system of bootstrap equations. Nevertheless, identification of these solution to the operators in terms of the basic fields remains problematic. In this work, we develop a technique of computing form factors of a class of CTO determined in terms of the basic field in the semiclassical approximation.