1+1 Gaudin Model

Abstract

We study 1+1 field-generalizations of the rational and elliptic Gaudin models. For $\mathrm{sl}(N)$ case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In $\mathrm{sl}(2)$ case we study the equations in detail and find the corresponding Hamiltonian densities. The $n$-site model describes $n$ interacting Landau-Lifshitz models of magnets. The interaction depends on position of the sites (marked points on the curve). We also analyze the 2-site case in its own right and describe its relation to the principal chiral model. We emphasize that 1+1 version impose a restriction on a choice of flows on the level of the corresponding 0+1 classical mechanics.

References in corpus (7)

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Cited by in corpus (10)

• Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
• Classical integrable systems and soliton equations related to eleven-vertex R-matrix
• Classification of Isomonodromy Problems on Elliptic Curves
• On the Zakharov-Mikhailov action: $4$d Chern-Simons origin and covariant Poisson algebra of the Lax connection
• Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
• Field theory generalizations of two-body Calogero-Moser models in the form of Landau-Lifshitz equations
• Resurgence in the Bi-Yang-Baxter Model
• Lax equations for relativistic $\mathrm{GL}(NM,\mathbb{C})$ Gaudin models on elliptic curve
• Tau-functions for Quiver Gauge Theories
• Multi-pole extension for elliptic models of interacting integrable tops