Integrability, conformal symmetry, and noncritical Virasoro algebras

We discuss the relation between integrability and conformal symmetry in the context of a unitary c = 1 lattice Virasoro algebra for the noncritical eight-vertex model. The lattice algebra is related to the critical conformal algebra by a modular transformation in spectral parameter (rapidity) space. Virasoro generators for massive free fermions are explicitly constructed in terms of integrals of local densities and a connection with higher conservation laws is exhibited. Comparing the Verma module states of the noncritical algebra with the Bethe ansatz states, we discuss a connection between the FQS discrete sequence and the bound state spectrum of the eight-vertex/massive-Thirring/sine-Gordon model. (orig.)