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arXiv · 2608.17837

Elliptic spin Ruijsenaars-Schneider integrable models from 5d $\mathcal{N}=1$ gauge theories

Gleb Arutyunov·Lukas Hardi
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Abstract

We show that the Coulomb branches of 5d $\mathcal{N}=1$ necklace quiver gauge theories on $\mathbb{R}^3 \times T^2$ are identified with the phase spaces of elliptic spin Ruijsenaars-Schneider models with dynamical inhomogeneities. This identification resolves the long-standing problem of determining a Poisson structure and a quantization of these models. We further show that the resulting quantum system is the integrable system governing supersymmetric indices of 4d $\mathcal{N}=1$ theories of class $\mathcal{S}_k$.

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Gleb Arutyunov, Lukas Hardi. 2026-08-18. Elliptic spin Ruijsenaars-Schneider integrable models from 5d $\mathcal{N}=1$ gauge theories. https://arxiv.org/abs/2608.17837

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