Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism

@misc{gu2026understanding,
  title = {{Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism}},
  author = {Zhenbang Gu and Ran Luo and Yi-Nan Wang and Yi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.08766},
  eprint = {2608.08766},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.08766},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism
AU  - Zhenbang Gu
AU  - Ran Luo
AU  - Yi-Nan Wang
AU  - Yi Zhang
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2608.08766
UR  - https://arxiv.org/abs/2608.08766
AB  - We present a systematic study of finite, non-split 2-group symmetries with a non-trivial Postnikov class, focusing on the simplest example with a ℤ_2 0-form symmetry and a ℤ_2 1-form symmetry, intertwined together by the non-trivial Postnikov class in H^3(Bℤ_2;ℤ_2)≅ℤ_2, denoted by 𝒢. We classify the anomalies of this 2-group symmetry for physical theories in d-dimensional spacetime, by computing the oriented bordism groups Ω_d+1^SO(B𝒢) and the spin bordism groups Ω_d+1^Spin(B𝒢) for d≤ 5. For the case of d=3, we investigate the Symmetry TFT/TO of the 2-group symmetry 𝒢 using the language of fusion 2-categories, as well as (3+1)D TQFT actions, for the cases without or with the 2-group anomaly classified by Hom(Ω̃_4^SO(B𝒢),U(1)) ≅ H^4(B𝒢;U(1))≅ℤ_2. We classify the minimal topological and physical boundary conditions of the Symmetry TFTs, and carry out the categorical Landau paradigm for such a non-split finite 2-group.
ER  -