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

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.