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.

12 pages. Minor corrections in Section 3

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• Poles of Painlevé IV Rationals and their Distribution
• Opers for higher states of quantum KdV models
• On the monodromy of the deformed cubic oscillator
• $QQ$-system and non-linear integral equations for scattering amplitudes at strong coupling
• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations
• TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics
• Stability conditions and cluster varieties from quivers of type $A$
• Painleve I, Coverings of the Sphere and Belyi Functions
• Quasi-exactly solvable quartic: real algebraic spectral locus
• The Direct Monodromy Problem of Painleve-I
• Two-parametric PT-symmetric quartic family