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We find the analytic expression of the trace of powers of the reduced densitymatrix on an interval of length L, for a massive boson field in 1+1 dimensions.This is given exactly (except for a non universal factor) in terms of a finitesum of solutions of non linear differential equations of the Painlev\'e V type.Our method is a generalization of one introduced by Myers and is based on theexplicit calculation of quantities related to the Green function on a plane,where boundary conditions are imposed on a finite cut. It is shown that theassociated partition function is related to correlators of exponentialoperators in the Sine-Gordon model in agreement with a result by Delfino et al.We also compute the short and long distance leading terms of the entanglemententropy. We find that the bosonic entropic c-function interpolates between theDirac and Majorana fermion ones given in a previous paper. Finally, we studysome universal terms for the entanglement entropy in arbitrary dimensionswhich, in the case of free fields, can be expressed in terms of the twodimensional entropy functions.Comment: 13 pages, 2 figure

Entanglement and alpha entropies for a massive scalar field in two dimensions