Supersymmetric extension of qKZ-Ruijsenaars correspondence

TL;DR

This paper establishes a supersymmetric extension of the qKZ-Ruijsenaars correspondence, linking quantum integrable models with supergroup symmetries and revealing invariance properties of their spectra.

Contribution

It introduces a supersymmetric generalization of the qKZ-Ruijsenaars correspondence, connecting supergroup-based quantum models with classical-quantum integrable systems.

Findings

Spectrum of Ruijsenaars-Schneider Hamiltonians is independent of ${f Z}_2$-grading.

Multiple qKZ systems correspond to the same quantum $n$-body problem.

Results extend classical-quantum correspondence to supersymmetric settings.

Abstract

We describe the correspondence of the Matsuo-Cherednik type between the quantum $n$-body Ruijsenaars-Schneider model and the quantum Knizhnik-Zamolodchikov equations related to supergroup $GL(N|M)$. The spectrum of the Ruijsenaars-Schneider Hamiltonians is shown to be independent of the ${\mathbb Z}_2$-grading for a fixed value of $N+M$, so that $N+M+1$ different qKZ systems of equations lead to the same $n$-body quantum problem. The obtained results can be viewed as a quantization of the previously described quantum-classical correspondence between the classical $n$-body Ruijsenaars-Schneider model and the supersymmetric $GL(N|M)$ quantum spin chains on $n$ sites.