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

Winding vacuum energies in a deformed O(4) sigma model