Massless Flows II:. the Exact S-Matrix Approach

We study the spectrum, the massless S matrices and the ground-state energy of the flows between successive minimal models of conformal field theory, and within the sine-Gordon model with imaginary coefficient of the cosine term (related to the minimal models by “truncation”). For the minimal models, we find exact S matrices which describe the scattering of massless kinks, and show using the thermodynamic Bethe ansatz that the resulting non-perturbative c function (defined by the Casimir energy on a cylinder) flows appropriately between the two theories, as conjectured earlier. For the nonunitary sine-Gordon model, we find unusual behavior. For the range of couplings we can study analytically, the natural S matrix deduced from the minimal one by “undoing” the quantum-group truncation does not reproduce the proper c function with the TBA. It does, however, describe the correct properties of the model in a magnetic field.