2026/07/30 by Gleb Arutyunov, Lukas Hardi, Rob Klabbers
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
17 pages, 3 figures, 1 table
arxiv created 2026/07/30 · arxiv updated 2026/07/31
We quantize the trigonometric spin Ruijsenaars-Schneider model of N particles each with ℓ spin states using the recently developed description of the classical model in terms of the K-theoretic Coulomb branch of the 4d N=2 quiver gauge theory for the necklace quiver with ℓ 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.