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arXiv · 2607.28043

Quantum Trigonometric Spin Ruijsenaars-Schneider Models from $K$-theoretic Coulomb Branches

Gleb Arutyunov·Lukas Hardi·Rob Klabbers
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Abstract

We quantize the trigonometric spin Ruijsenaars-Schneider model of $N$ particles each with $\ell$ spin states using the recently developed description of the classical model in terms of the $K$-theoretic Coulomb branch of the 4d $\mathcal{N}=2$ quiver gauge theory for the necklace quiver with $\ell$ nodes of rank $N$. The main algebraic tool is an algebra of $L$-operators derived from abelianized monopole operators of minuscule charge, which turns the necklace quiver into an integrable spin chain by producing a family of commuting Hamiltonians. We show that the lowest Hamiltonian coincides with the first mode of the quantum determinant of the horizontal quantum loop algebra living inside the $K$-theoretic Coulomb branch algebra, whose Bethe subalgebra generates a maximal family of commuting Hamiltonians. Finally, we derive the commutation relations and quantum equations of motion of the quantized physical spin variables.

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Gleb Arutyunov, Lukas Hardi, Rob Klabbers. 2026-07-30. Quantum Trigonometric Spin Ruijsenaars-Schneider Models from $K$-theoretic Coulomb Branches. https://arxiv.org/abs/2607.28043

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