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PreprintarXiv licencearXiv

Elliptic spin Ruijsenaars-Schneider integrable models from 5d 𝒩=1 gauge theories

  • Gleb Arutyunov
  • Lukas Hardi
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Abstract

We show that the Coulomb branches of 5d 𝒩=1 necklace quiver gauge theories on ℝ3 × T2 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 𝒩=1 theories of class 𝒮k.

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Cite

BibTeXRIS
BibTeX
@misc{arutyunov2026elliptic,
  title = {{Elliptic spin Ruijsenaars-Schneider integrable models from 5d $\mathcalN=1$ gauge theories}},
  author = {Gleb Arutyunov and Lukas Hardi},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.17837},
  eprint = {2608.17837},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.17837},
}
RIS
TY  - UNPB
TI  - Elliptic spin Ruijsenaars-Schneider integrable models from 5d 𝒩=1 gauge theories
AU  - Gleb Arutyunov
AU  - Lukas Hardi
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.17837
UR  - https://arxiv.org/abs/2608.17837
AB  - We show that the Coulomb branches of 5d 𝒩=1 necklace quiver gauge theories on ℝ^3 × 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 𝒩=1 theories of class 𝒮_k.
ER  -