Large N limit of spectral duality in classical integrable systems

2025/08/22 by Potapov, R., Zotov, A. · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2508.16470

Abstract

We describe the large N limit of spectral duality between rational Gaudin models introduced by Adams, Harnad and Hurtubise. The limit of the \rm 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 \rm gl_M Gaudin model with N marked points written in the form of the Gaudin model with irregular singularities.

Citations

• Quantum geometry and quiver gauge theories
• A generalization of the Capelli identity
• Bispectral and (gl_N, gl_M) Dualities, Discrete Versus Differential
• Duality of spectral curves arising in two-matrix models
• Quantum mechanics as a statistical theory

Cited by

• Large N limit of spectral duality between the classical XXX spin chain and the rational reduced Gaudin model

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