Supersymmetric extension of qKZ-Ruijsenaars correspondence

A. Grekov, A. Zabrodin, A. Zotov

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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 Z2-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.

Original languageEnglish
Pages (from-to)174-190
Number of pages17
JournalNuclear Physics B
Volume939
DOIs
Publication statusPublished - Feb 2019

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