CENTRAL CHARGES WITHOUT FINITE-SIZE EFFECTS

We show how to obtain the ultraviolet central charge from the exact S-matrix for a wide variety of models with a U(1) symmetry. This is done by coupling the U(1) current J to a background field. In an N=2 superconformal theory with J the fermion number current, the OPE of J with itself and hence the free energy are proportional to c. By deforming the supersymmetry into affine su(2)q quantum-group symmetry, this result can be generalized to many U(1) -invariant theories, including the N=0 and N=1 sine-Gordon models and the SU(2)k WZW models. This provides a consistency check on a conjectured S-matrix completely independent of the finite-size effects expressed in terms of dilogarithms resulting from the thermodynamic Bethe ansatz.