  We study the scaling limit of a fully packed loop model in two dimensions,
where the loops are endowed with a bending rigidity. The scaling limit is
described by a three-parameter family of conformal field theories, which we
characterize via its Coulomb-gas representation. One choice for two of the
three parameters reproduces the critical line of the exactly solvable
six-vertex model, while another corresponds to the Flory model of polymer
melting. Exact central charge and critical exponents are calculated for polymer
melting in two dimensions. Contrary to predictions from mean-field theory we
show that polymer melting, as described by the Flory model, is continuous. We
test our field theoretical results against numerical transfer matrix
calculations.
