On vacuum energies and renormalizability in integrable quantum field   theories
  We compute for various perturbed conformal field theories the vacuum energies by means of the thermodynamic Bethe ansatz. Depending on the infrared and ultraviolet divergencies of the models, governed by the scaling dimensions of the underlying perturbed conformal field theory in the ultraviolet, the vacuum energies exhibit different types of characteristics. In particular, for the homogeneous sine-Gordon models we observe that once the conformal dimension of the perturbing scalar field is smaller or greater than 1/2, the vacuum energies are positive or negative, respectively. This behaviour indicates the need for additional ultraviolet counterterms in the latter case. At the transition points we obtain an infinite vacuum energy, which is partly explainable with the presence of several free Fermions in the models studied. 
Olalla Castro-Alvaredo and Andreas Fring