ODE/IQFT correspondence for the generalized affine $\mathfrak{sl}(2)$ Gaudin model

Abstract

An integrable system is introduced, which is a generalization of the $\mathfrak{sl}(2)$ quantum affine Gaudin model. Among other things, the Hamiltonians are constructed and their spectrum is calculated within the ODE/IQFT approach. The model fits within the framework of Yang-Baxter integrability. This opens a way for the systematic quantization of a large class of integrable non-linear sigma models. There may also be some interest in terms of Condensed Matter applications, as the theory can be thought of as a multiparametric generalization of the Kondo model.

arXiv commentv2: 75 pages, 2 tables, 6 figures, minor typos corrected, published version

References in corpus (31)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Gaudin Model, Bethe Ansatz and Critical Level
• Exact non-equilibrium transport through point contacts in quantum wires and fractional quantum Hall devices
• Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
• Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory
• A unified framework for the Kondo problem and for an impurity in a Luttinger liquid
• Assembling integrable sigma-models as affine Gaudin models
• An exact solution method for 1D polynomial Schrödinger equations
• Integrable coupled sigma-models
• Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states
• The $Z_2$ staggered vertex model and its applications
• Gauss decomposition of trigonometric R-matrices
• Integrable Circular Brane Model and Coulomb Charging at Large Conduction
• Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model
• Notes on parafermionic QFT's with boundary interaction
• Analytical results for the Coqblin-Schrieffer model with generalized magnetic fields
• Liouville reflection operator, affine Yangian and Bethe ansatz
• Higher-level eigenvalues of Q-operators and Schroedinger equation
• ODE/IM correspondence for the Fateev model
• Integrable Kondo problems
• TBA equations for the Schrödinger equation with a regular singularity
• Quantum transfer-matrices for the sausage model
• Integrable boundary interaction in 3D target space: the "pillow-brane" model
• Spectrum of the reflection operators in different integrable structures
• Bethe state norms for the Heisenberg spin chain in the scaling limit
• Exact resolution method for general 1D polynomial Schrödinger equation
• Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model
• Rational maps as Schwarzian primitives