  We consider the problem of calculating the Casimir energies in the winding
sectors of Fateev's SS-model, which is an integrable two-parameter deformation
of the O(4) non-linear sigma model in two dimensions. This problem lies beyond
the scope of all traditional methods of integrable quantum field theory
including the thermodynamic Bethe ansatz and non-linear integral equations.
Here we propose a solution based on a remarkable correspondence between
classical and quantum integrable systems and express the winding energies in
terms of certain solutions of the classical sinh-Gordon equation.
