arXiv subjects

Lukas Hardi

Publications and source records attributed to Lukas Hardi.

4 recordsLinked to original sources

arXiv2026

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

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 $\mathcal{S}_k$.

hep-th↗

arXiv2026

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

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.

hep-th↗

arXiv2026

Spin Ruijsenaars-Schneider models are Coulomb branches

In this paper, we show that the Poisson algebras of homological and $K$-theoretic Coulomb branches of 3d $\mathcal{N}=4$ necklace quiver gauge theories provide Poisson structures and Hamiltonians that reproduce the equations of motion of the rational and hyperbolic spin Ruijsenaars-Schneider models, respectively. The construction is carried out in terms of monopole operators in the GKLO representation, also making the affine Yangian (and, in $K$-theory, quantum toroidal) superintegrability structure manifest. We conjecture that the Poisson algebras of elliptic Coulomb branches similarly reproduce the elliptic spin Ruijsenaars-Schneider model.

hep-th↗

arXiv2025

Quantized Quiver Varieties and the Quantum Spin Ruijsenaars-Schneider Model

This paper tackles the long-standing problem of quantizing the rational spin Ruijsenaars--Schneider model originating in the work of Krichever and Zabrodin. We make use of the technique of quantum Hamiltonian reduction to construct a quantized quiver variety $\mathfrak{A}_{N,\ell}$ associated to the framed Jordan quiver. This quantized quiver variety is simultaneously the algebra of quantum observables of the rational spin Ruijsenaars--Schneider model of $N$ particles with $\ell$ spin polarizations. Inside this algebra, we find a loop algebra and Yangian of $\mathfrak{gl}_\ell$ and conjecture that in the limit of infinitely many particles, the algebra $\mathfrak{A}_{N,\ell}$ becomes a shifted affine Yangian. We also exhibit a difference equation for eigenstates of the lowest Hamiltonian that reduces to the spinless case when $\ell=1$.

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