Large N limit of spectral duality in classical integrable systems

Abstract

We describe the large $N$ limit of spectral duality between rational Gaudin models introduced by Adams, Harnad and Hurtubise. The limit of the ${\mathrm{gl}}_N$ model is performed by means of a noncommutative torus algebra represented by the fields on a torus with the Moyal-Weyl star product. We apply the approach developed by Hoppe, Olshanetsky and Theisen to the Gaudin-type models and describe the corresponding integrable field theory (2d hydrodynamics) on a torus. The dual model is the large $N$ limit of the ${\mathrm{gl}}_M$ Gaudin model with $N$ marked points written in the form of the Gaudin model with irregular singularities.

20 pages, minor corrections

References in corpus (14)

• Noncommutative Field Theory
• Gaudin Model, Bethe Ansatz and Critical Level
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• Duality, Biorthogonal Polynomials and Multi-Matrix Models
• Gaudin models with irregular singularities
• Explicit examples of DIM constraints for network matrix models
• Spectral Duality in Integrable Systems from AGT Conjecture
• Spectral Duality Between Heisenberg Chain and Gaudin Model
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Relativistic Classical Integrable Tops and Quantum R-matrices
• Spectral dualities in XXZ spin chains and five dimensional gauge theories
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Spectral curve duality beyond the two-matrix model
• Interrelations between dualities in classical integrable systems and classical-classical version of quantum-classical duality