  By viewing the Sine-Gordon and massive Thirring models as perturbed conformal
field theories one sees that they are different (the difference being
observable, for instance, in finite-volume energy levels). The UV limit of the
former (SGM) is a gaussian model, that of the latter (MTM) a so-called {\it
fermionic} gaussian model, the compactification radius of the boson underlying
both theories depending on the SG/MT coupling. (These two families of conformal
field theories are related by a ``twist''.) Corresponding SG and MT models
contain a subset of fields with identical correlation functions, but each model
also has fields the other one does not, e.g. the fermion fields of MTM are not
contained in SGM, and the {\it bosonic} soliton fields of SGM are not in MTM.
Our results imply, in particular, that the SGM at the so-called ``free-Dirac
point'' $\beta^2 = 4\pi$ is actually a theory of two interacting bosons with
diagonal S-matrix $S=-1$, and that for arbitrary couplings the overall sign of
the accepted SG S-matrix in the soliton sector should be reversed. More
generally, we draw attention to the existence of new classes of quantum field
theories, analogs of the (perturbed) fermionic gaussian models, whose partition
functions are invariant only under a subgroup of the modular group. One such
class comprises ``fermionic versions'' of the Virasoro minimal models.
