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Peer-reviewedCC BY 4.0SciPost Physics

Spin chains for ADE quiver theories

  • Jarryd Bath1
  • Konstantinos Zoubos2,1
  1. 1University of Pretoria
  2. 2National Institute for Theoretical and Computational Sciences
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Abstract

The spectral problem of four-dimensional superconformal quiver gauge theories can be mapped to one-dimensional spin chains with restricted Hilbert spaces, where the composition of neighbouring spins follows the path algebra of the quiver. To better understand such spin chains, we compute the one-loop planar dilatation operator for the 4d \mathcal{N}=2 𝒩 = 2 ADE quiver gauge theories obtained by orbifolding the \mathcal{N}=4 𝒩 = 4 Super-Yang-Mills theory and marginally deforming by independently varying the gauge couplings. This extends previous work which was mainly focused on the \mathbb{Z}_2 ℤ 2 quiver. We characterise the general features of the resulting ADE spin-chain models and construct the 2-magnon Bethe Ansatz for holomorphic states. We also evaluate, at large N N , the \mathcal{N}=2 𝒩 = 2 superconformal index of these gauge theories and use it to study their protected spectrum in specific sectors.

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Cite

BibTeXRIS
BibTeX
@article{bath2026spin,
  title = {{Spin chains for ADE quiver theories}},
  author = {Jarryd Bath and Konstantinos Zoubos},
  journal = {SciPost Physics},
  year = {2026},
  month = oct,
  doi = {10.21468/scipostphys.21.4.091},
  url = {https://scipost.org/10.21468/SciPostPhys.21.4.091},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Spin chains for ADE quiver theories
AU  - Jarryd Bath
AU  - Konstantinos Zoubos
PY  - 2026
DA  - 2026/10/12
JO  - SciPost Physics
DO  - 10.21468/scipostphys.21.4.091
UR  - https://scipost.org/10.21468/SciPostPhys.21.4.091
AB  - The spectral problem of four-dimensional superconformal quiver gauge theories can be mapped to one-dimensional spin chains with restricted Hilbert spaces, where the composition of neighbouring spins follows the path algebra of the quiver. To better understand such spin chains, we compute the one-loop planar dilatation operator for the 4d \mathcal{N}=2 𝒩 = 2 ADE quiver gauge theories obtained by orbifolding the \mathcal{N}=4 𝒩 = 4 Super-Yang-Mills theory and marginally deforming by independently varying the gauge couplings. This extends previous work which was mainly focused on the \mathbb{Z}_2 ℤ 2 quiver. We characterise the general features of the resulting ADE spin-chain models and construct the 2-magnon Bethe Ansatz for holomorphic states. We also evaluate, at large N N , the \mathcal{N}=2 𝒩 = 2 superconformal index of these gauge theories and use it to study their protected spectrum in specific sectors.
SN  - 2542-4653
ER  -