Composite branch-point twist fields in the Ising model and their expectation values

TL;DR

This paper calculates the exact two-point correlation function involving the energy and twist fields in the n-copy Ising model, revealing the structure of the short-distance operator product expansion and expectation values.

Contribution

It provides an exact integral representation and short-distance expansion of the correlation function, identifying contributing fields and their expectation values in the Ising model.

Findings

Exact integral representation of the correlation function

Identification of fields in the short-distance OPE

Determination of expectation values and form factors

Abstract

We investigate a particular two-point function of the $n$-copy Ising model. That is, the correlation function $\vev{\E(r)\T(0)}$ involving the energy field and the branch-point twist field. The latter is associated to the symmetry of the theory under cyclic permutations of its copies. We use a form factor expansion to obtain an exact integral representation of $\vev{\E(r)\T(0)}$ and find its complete short distance expansion. This allows us to identify all the fields contributing in the short distance massive OPE of the correlation function under examination, and fix their expectation values, conformal structure constants and massive corrections thereof. Most contributions are given by the composite field $:\E\T:$ and its derivatives. We find all non-vanishing form factors of this latter operator.