Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 41 min ago
Peer-reviewedCC BY 4.0SciPost

On non-relativistic integrable models and 4d SCFTs

  • Rotem Ben Zeev1
  • Anirudh Deb2
  • Hee-Cheol Kim3,4
  • Shlomo S. Razamat1
4 affiliations
  1. 1Department of Physics, Technion
  2. 2C.N. Yang Institute for Theoretical Physics
  3. 3Asia Pacific Center for Theoretical Physics
  4. 4Pohang University of Science and Technology
Open at sourcePDFDOICite

Abstract

We elaborate on the relation between the generalized Schur index of {\cal 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 {\cal S} in terms of elliptic Jack functions. For example, in the A_1 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 {\cal 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 Q E-string theory. We argue that in general the “Schur index” of {\cal N}=1 4d 4 d SCFTs can be understood as being related to the free fermionic limit of a non-relativistic integrable model.

Related

  1. 6d SCFTs and terminal singularities
    Andrea Sangiovanni
    arXivPreprintCC BY 4.0Full textHigh-energy & particle physicsarXiv
  2. Quantum curves of 6d SCFTs on a -3 curve
    Minsung Kim, Sung-Soo Kim, Xin Wang
    arXivPreprintCC BY 4.0Full textHigh-energy & particle physicsarXiv
  3. Supersymmetric Observables from Surface Defect Anomalies in 4d and 6d SCFTs
    Zi-Xiao Huang, Ma-Ke Yuan, Yang Zhou
    arXivPreprintarXiv licenceFull textMathematical physicsCondensed matterarXiv
  4. Wilson line defect indices for M2-brane SCFTs
    Hirotaka Hayashi, Tomoki Nosaka, Tadashi Okazaki
    arXivPreprintarXiv licenceFull textHigh-energy & particle physicsarXiv
  5. Dualities, symmetries and the elliptic genus of 2d (0,2) SCFTs
    Salomon Malka, Gabi Zafrir
    arXivPreprintarXiv licenceFull textHigh-energy & particle physicsarXiv

Cite

BibTeXRIS
BibTeX
@article{zeev2026nonrelativistic,
  title = {{On non-relativistic integrable models and 4d SCFTs}},
  author = {Rotem Ben Zeev and Anirudh Deb and Hee-Cheol Kim and Shlomo S. Razamat},
  journal = {SciPost},
  year = {2026},
  month = nov,
  doi = {10.21468/scipostphys.21.5.110},
  url = {http://scipost.org/SciPostPhys.21.5.110},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - On non-relativistic integrable models and 4d SCFTs
AU  - Rotem Ben Zeev
AU  - Anirudh Deb
AU  - Hee-Cheol Kim
AU  - Shlomo S. Razamat
PY  - 2026
DA  - 2026/11/02
JO  - SciPost
DO  - 10.21468/scipostphys.21.5.110
UR  - http://scipost.org/SciPostPhys.21.5.110
AB  - We elaborate on the relation between the generalized Schur index of {\cal 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 {\cal S} in terms of elliptic Jack functions. For example, in the A_1 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 {\cal 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 Q E-string theory. We argue that in general the “Schur index” of {\cal N}=1 4d 4 d SCFTs can be understood as being related to the free fermionic limit of a non-relativistic integrable model.
SN  - 2542-4653
ER  -