Entanglement entropy of two disjoint intervals in conformal field theory

We study the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson). Tr ρAn for any integer n is calculated as the four-point function of twist fields of a particular type and the final result is expressed in a compact form in terms of the Riemann–Siegel theta functions. In the decompactification limit we provide the analytic continuation valid for all model parameters and from this we extract the entanglement entropy. These predictions are checked against existing numerical data