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PreprintCC BY 4.0arXiv

Difference between pair creation and anomaly matching: Nontrivial aspects of invertible symmetries and defects in SU(N) models

  • Yoshiki Fukusumi
  • Shuma Nakashiba
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Abstract

We study the connection between the SU(N)K Wess-Zumino-Witten (WZW) model and SU(N)K' WZW model, enforcing the ℤN symmetries. The fundamental underlying structures are the (half-)integer spin simple currents in the topological quantum field theories and anomaly matching conditions in conformal field theories. For the (half-)integer spin simple current condition, we obtain the generalized pairing condition K= ± R2K' (mod.N) with gcd(R,N)=1. On the other hand, the anomaly matching condition results in the weaker condition K= ± RUK' (mod.N) with gcd(R,N)=gcd(U,N)=1. The preservation law of the ℤN defects and symmetries is compatible only with the pairing condition.

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Cite

BibTeXRIS
BibTeX
@misc{fukusumi2026difference,
  title = {{Difference between pair creation and anomaly matching: Nontrivial aspects of invertible symmetries and defects in $SU(N)$ models}},
  author = {Yoshiki Fukusumi and Shuma Nakashiba},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21478},
  eprint = {2610.21478},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21478},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Difference between pair creation and anomaly matching: Nontrivial aspects of invertible symmetries and defects in SU(N) models
AU  - Yoshiki Fukusumi
AU  - Shuma Nakashiba
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.21478
UR  - https://arxiv.org/abs/2610.21478
AB  - We study the connection between the SU(N)_K Wess-Zumino-Witten (WZW) model and SU(N)_K' WZW model, enforcing the ℤ_N symmetries. The fundamental underlying structures are the (half-)integer spin simple currents in the topological quantum field theories and anomaly matching conditions in conformal field theories. For the (half-)integer spin simple current condition, we obtain the generalized pairing condition K= ± R^2K' (mod.N) with gcd(R,N)=1. On the other hand, the anomaly matching condition results in the weaker condition K= ± RUK' (mod.N) with gcd(R,N)=gcd(U,N)=1. The preservation law of the ℤ_N defects and symmetries is compatible only with the pairing condition.
ER  -