ODE/IM correspondence for the Fateev model

Abstract

The Fateev model is somewhat special among two-dimensional quantum field theories. For different values of the parameters,it can be reduced to a variety of integrable systems. An incomplete list of the reductions includes O(3) and O(4) non-linear sigma models and their continuous deformations (2D and 3D sausages, anisotropic principal chiral field), the Bukhvostov-Lipatov model, the N=2 supersymmetric sine-Gordon model, as well as the integrable perturbed SU_2(n)\otimes SU_2(p-2)/SU_2(n+p-2) coset CFT. The model possesses a mysterious symmetry structure of the exceptional quantum superalgebras U_q{\hat{\big(D(2|1;α)}}\big). In this work, we propose the ODE/IM correspondence between the Fateev model and a certain generalization of the classical problem of constant mean curvature embedding of a thrice-punctured sphere in AdS_3.

28 pages, 4 figures

References in corpus (4)

• The ODE/IM Correspondence
• Notes on parafermionic QFT's with boundary interaction
• The Bethe Ansatz and the Tzitzéica-Bullough-Dodd equation
• Integrable boundary interaction in 3D target space: the "pillow-brane" model

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• On spectrum of ILW hierarchy in conformal field theory II: coset CFT's
• Affine Yangian of $\mathfrak{gl}(2)$ and integrable structures of superconformal field theory
• Quantum transfer-matrices for the sausage model
• Winding vacuum energies in a deformed O(4) sigma model
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
• 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
• From Fuchsian differential equations to integrable QFT
• Feigin-Frenkel-Hernandez Opers and the QQ-system
• The sausage sigma model revisited
• ODE/IQFT correspondence for the generalized affine $\mathfrak{sl}(2)$ Gaudin model