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

Abstract

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.

arXiv comment10 pages, 4 figures

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• Geometric aspects of the ODE/IM correspondence
• Quantum transfer-matrices for the sausage model
• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations
• Bukhvostov-Lipatov model and quantum-classical duality
• Vacuum energy of the Bukhvostov-Lipatov model
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