Anomalies of Coset Non-Invertible Symmetries
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908760675450880 |
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| author | Hsin, Po-Shen Kobayashi, Ryohei Zhang, Carolyn |
| author_facet | Hsin, Po-Shen Kobayashi, Ryohei Zhang, Carolyn |
| contents | Anomalies of global symmetries provide important information on the quantum dynamics. We show the dynamical constraints can be organized into three classes: genuine anomalies, fractional topological responses, and integer responses that can be realized in symmetry-protected topological (SPT) phases. Coset symmetry can be present in many physical systems including quantum spin liquids, and the coset symmetry can be a non-invertible symmetry. We introduce twists in coset symmetries, which modify the fusion rules and the generalized Frobenius-Schur indicators. We call such coset symmetries twisted coset symmetries, and they are labeled by the quadruple $(G,K,ω_{D+1},α_D)$ in $D$ spacetime dimensions where $G$ is a group and $K\subset G$ is a discrete subgroup, $ω_{D+1}$ is a $(D+1)$-cocycle for group $G$, and $α_{D}$ is a $D$-cochain for group $K$. We present several examples with twisted coset symmetries using lattice models and field theory, including both gapped and gapless systems (such as gapless symmetry-protected topological phases). We investigate the anomalies of general twisted coset symmetry, which presents obstructions to realizing the coset symmetry in (gapped) symmetry-protected topological phases. We show that finite coset symmetry $G/K$ becomes anomalous when $G$ cannot be expressed as the bicrossed product $G=H\Join K$, and such anomalous coset symmetry leads to symmetry-enforced gaplessness in generic spacetime dimensions. We illustrate examples of anomalous coset symmetries with $A_5/\mathbb{Z}_2$ symmetry, with realizations in lattice models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anomalies of Coset Non-Invertible Symmetries Hsin, Po-Shen Kobayashi, Ryohei Zhang, Carolyn Strongly Correlated Electrons High Energy Physics - Theory Quantum Algebra Anomalies of global symmetries provide important information on the quantum dynamics. We show the dynamical constraints can be organized into three classes: genuine anomalies, fractional topological responses, and integer responses that can be realized in symmetry-protected topological (SPT) phases. Coset symmetry can be present in many physical systems including quantum spin liquids, and the coset symmetry can be a non-invertible symmetry. We introduce twists in coset symmetries, which modify the fusion rules and the generalized Frobenius-Schur indicators. We call such coset symmetries twisted coset symmetries, and they are labeled by the quadruple $(G,K,ω_{D+1},α_D)$ in $D$ spacetime dimensions where $G$ is a group and $K\subset G$ is a discrete subgroup, $ω_{D+1}$ is a $(D+1)$-cocycle for group $G$, and $α_{D}$ is a $D$-cochain for group $K$. We present several examples with twisted coset symmetries using lattice models and field theory, including both gapped and gapless systems (such as gapless symmetry-protected topological phases). We investigate the anomalies of general twisted coset symmetry, which presents obstructions to realizing the coset symmetry in (gapped) symmetry-protected topological phases. We show that finite coset symmetry $G/K$ becomes anomalous when $G$ cannot be expressed as the bicrossed product $G=H\Join K$, and such anomalous coset symmetry leads to symmetry-enforced gaplessness in generic spacetime dimensions. We illustrate examples of anomalous coset symmetries with $A_5/\mathbb{Z}_2$ symmetry, with realizations in lattice models. |
| title | Anomalies of Coset Non-Invertible Symmetries |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2503.00105 |