Non-invertible symmetries and mixed anomalies from conserved current construction in (3+1)D twisted $BF$ topological quantum field theories
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912880571449344 |
|---|---|
| author | Zhang, Zhi-Feng Huang, Yizhou Wang, Qing-Rui Ye, Peng |
| author_facet | Zhang, Zhi-Feng Huang, Yizhou Wang, Qing-Rui Ye, Peng |
| contents | We develop a current-based construction of generalized symmetries in $(3+1)$D twisted $BF$ topological quantum field theories (TQFTs), focusing on intrinsically non-invertible higher-form symmetries and their mixed anomalies. Starting from the equations of motion, we extract conserved currents and exponentiate the corresponding charges to obtain topological symmetry operators. This gives a step-by-step procedure for constructing symmetry operators, fusion, and anomaly diagnostics directly from the continuum action. We focus on twisted $BF$ theories with gauge group $G=\prod_i \mathbb{Z}_{N_i}$ and an $a\wedge a\wedge b$ twist, where $a$'s and $b$ are 1-form and 2-form gauge fields, respectively. These theories realize non-Abelian $(3+1)$D TQFTs supporting Borromean-rings braiding and describe three-dimensional non-Abelian topological orders in condensed matter. For $G=(\mathbb{Z}_2)^3$, a microscopic realization is given by the $\mathbb{D}_4$ Kitaev quantum double model. Two distinct classes of conserved currents emerge: Type-I currents generate invertible higher-form symmetries with group-like fusion, while Type-II currents require additional consistency conditions on gauge-field configurations, leading to intrinsically non-invertible symmetries dressed by projectors. We compute the fusion algebra: invertible operators admit inverses, while non-invertible ones exhibit multi-channel fusion governed by projector fusion. We diagnose mixed anomalies by coupling multiple conserved currents to background gauge fields, revealing two outcomes: anomalies canceled by anomaly inflow from a higher-dimensional theory, and intrinsic gauging obstructions encoded in the $(3+1)$D continuum theory. Overall, our results provide a unified and practical approach for constructing and characterizing higher-form symmetries, which can be extended to more general TQFTs and topological orders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01523 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-invertible symmetries and mixed anomalies from conserved current construction in (3+1)D twisted $BF$ topological quantum field theories Zhang, Zhi-Feng Huang, Yizhou Wang, Qing-Rui Ye, Peng Strongly Correlated Electrons High Energy Physics - Theory We develop a current-based construction of generalized symmetries in $(3+1)$D twisted $BF$ topological quantum field theories (TQFTs), focusing on intrinsically non-invertible higher-form symmetries and their mixed anomalies. Starting from the equations of motion, we extract conserved currents and exponentiate the corresponding charges to obtain topological symmetry operators. This gives a step-by-step procedure for constructing symmetry operators, fusion, and anomaly diagnostics directly from the continuum action. We focus on twisted $BF$ theories with gauge group $G=\prod_i \mathbb{Z}_{N_i}$ and an $a\wedge a\wedge b$ twist, where $a$'s and $b$ are 1-form and 2-form gauge fields, respectively. These theories realize non-Abelian $(3+1)$D TQFTs supporting Borromean-rings braiding and describe three-dimensional non-Abelian topological orders in condensed matter. For $G=(\mathbb{Z}_2)^3$, a microscopic realization is given by the $\mathbb{D}_4$ Kitaev quantum double model. Two distinct classes of conserved currents emerge: Type-I currents generate invertible higher-form symmetries with group-like fusion, while Type-II currents require additional consistency conditions on gauge-field configurations, leading to intrinsically non-invertible symmetries dressed by projectors. We compute the fusion algebra: invertible operators admit inverses, while non-invertible ones exhibit multi-channel fusion governed by projector fusion. We diagnose mixed anomalies by coupling multiple conserved currents to background gauge fields, revealing two outcomes: anomalies canceled by anomaly inflow from a higher-dimensional theory, and intrinsic gauging obstructions encoded in the $(3+1)$D continuum theory. Overall, our results provide a unified and practical approach for constructing and characterizing higher-form symmetries, which can be extended to more general TQFTs and topological orders. |
| title | Non-invertible symmetries and mixed anomalies from conserved current construction in (3+1)D twisted $BF$ topological quantum field theories |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.01523 |