On non-relativistic integrable models and 4d SCFTs

Fuente: arXiv
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Main Authors: Zeev, Rotem Ben, Deb, Anirudh, Kim, Hee-Cheol, Razamat, Shlomo S.
Format: Preprint
Published: 2026
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author Zeev, Rotem Ben
Deb, Anirudh
Kim, Hee-Cheol
Razamat, Shlomo S.
author_facet Zeev, Rotem Ben
Deb, Anirudh
Kim, Hee-Cheol
Razamat, Shlomo S.
contents We elaborate on the relation between the generalized Schur index of $N=2$ SCFTs in four dimensions and the non-relativistic limit of the elliptic Ruijsenaars-Schneider model. In particular we discuss explicitly how to express generalized Schur indices of theories of class $S$ in terms of elliptic Jack functions. For example, in the $A_1$ case the indices are given naturally in terms of eigenfunctions of the Lamé equation. We use the expression in terms of eigenfunctions to further check the recent observation that the generalized Schur indices of different theories in the Deligne-Cvitanović series can be mapped onto each other. This mapping implies non trivial identities on unrefined sums of eigenfunctions of non-relativistic elliptic Calogero-Moser models associated to different root systems. We claim then that the non-relativistic limits of various integrable models give rise naturally to generalized Schur-like limits of classes of $N=1$ SCFTs. As an example we discuss the relation of the Inozemtsev model, the non relativistic limit of the van Diejen model, and compactifications of the rank $Q$ E-string theory. We argue that in general the ``Schur index'' of $N=1$ $4d$ SCFTs can be understood as being related to the free fermionic limit of a non-relativistic integrable model.
format Preprint
id arxiv_https___arxiv_org_abs_2604_19885
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On non-relativistic integrable models and 4d SCFTs
Zeev, Rotem Ben
Deb, Anirudh
Kim, Hee-Cheol
Razamat, Shlomo S.
High Energy Physics - Theory
Mathematical Physics
We elaborate on the relation between the generalized Schur index of $N=2$ SCFTs in four dimensions and the non-relativistic limit of the elliptic Ruijsenaars-Schneider model. In particular we discuss explicitly how to express generalized Schur indices of theories of class $S$ in terms of elliptic Jack functions. For example, in the $A_1$ case the indices are given naturally in terms of eigenfunctions of the Lamé equation. We use the expression in terms of eigenfunctions to further check the recent observation that the generalized Schur indices of different theories in the Deligne-Cvitanović series can be mapped onto each other. This mapping implies non trivial identities on unrefined sums of eigenfunctions of non-relativistic elliptic Calogero-Moser models associated to different root systems. We claim then that the non-relativistic limits of various integrable models give rise naturally to generalized Schur-like limits of classes of $N=1$ SCFTs. As an example we discuss the relation of the Inozemtsev model, the non relativistic limit of the van Diejen model, and compactifications of the rank $Q$ E-string theory. We argue that in general the ``Schur index'' of $N=1$ $4d$ SCFTs can be understood as being related to the free fermionic limit of a non-relativistic integrable model.
title On non-relativistic integrable models and 4d SCFTs
topic High Energy Physics - Theory
Mathematical Physics
url https://arxiv.org/abs/2604.19885