Y-System and Deformed Thermodynamic Bethe Ansatz

Abstract: We introduce a new tool, the Deformed TBA (Deformed Thermodynamic Bethe Ansatz), to analyze the monodromy problem of the cubic oscillator. The Deformed TBA is a system of five coupled nonlinear integral equations, which in a particular case reduces to the Zamolodchikov TBA equation for the 3-state Potts model. Our method generalizes the Dorey-Tateo analysis of the (monomial) cubic oscillator. We introduce a Y-system corresponding to the Deformed TBA and give it an elegant geometric interpretation.