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PreprintCC BY 4.0arXiv

Chern-Simons Interfaces and Minimal Models from Quantum Groups

  • Suriyah Rajalingam Kannagi
  • Sergio Sanjurjo
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Abstract

Coupling two-dimensional fundamental Dirac fermions to SU(N)k Chern-Simons theory produces non-chiral interfaces that in the infrared flow to a compact boson and a WN minimal model. We propose a description of these interfaces as continuum limits of q-deformed fermion chains. The q-deformation is achieved by coupling a chain of one-dimensional fundamental complex fermions to SU(N)k Chern-Simons theory, keeping the underlying topological gauge field continuous. The operator algebra is controlled by quantum groups, which provide an algebraic perspective on the usual categorical formulation of anyon chains. As an application, we derive a Lieb-Schultz-Mattis constraint involving baryon-number and lattice translation, obstructing a unique symmetric gapped ground state. At unit filling, we gap out the compact boson sector with a Mott term and obtain standard anyon chain Hamiltonians previously studied in the literature. This provides an anomaly argument for the existence of N copies of minimal model sectors permuted by lattice translation in the infrared.

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Cite

BibTeXRIS
BibTeX
@misc{kannagi2026chernsimons,
  title = {{Chern-Simons Interfaces and Minimal Models from Quantum Groups}},
  author = {Suriyah Rajalingam Kannagi and Sergio Sanjurjo},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07012},
  eprint = {2611.07012},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07012},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Chern-Simons Interfaces and Minimal Models from Quantum Groups
AU  - Suriyah Rajalingam Kannagi
AU  - Sergio Sanjurjo
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.07012
UR  - https://arxiv.org/abs/2611.07012
AB  - Coupling two-dimensional fundamental Dirac fermions to SU(N)_k Chern-Simons theory produces non-chiral interfaces that in the infrared flow to a compact boson and a W_N minimal model. We propose a description of these interfaces as continuum limits of q-deformed fermion chains. The q-deformation is achieved by coupling a chain of one-dimensional fundamental complex fermions to SU(N)_k Chern-Simons theory, keeping the underlying topological gauge field continuous. The operator algebra is controlled by quantum groups, which provide an algebraic perspective on the usual categorical formulation of anyon chains. As an application, we derive a Lieb-Schultz-Mattis constraint involving baryon-number and lattice translation, obstructing a unique symmetric gapped ground state. At unit filling, we gap out the compact boson sector with a Mott term and obtain standard anyon chain Hamiltonians previously studied in the literature. This provides an anomaly argument for the existence of N copies of minimal model sectors permuted by lattice translation in the infrared.
ER  -