Anomalies of coset non-invertible symmetries, by Po-Shen Hsin, Ryohei Kobayashi, Carolyn Zhang

SciPost Physics Home Authoring Refereeing Submit a manuscript About Anomalies of coset non-invertible symmetries Po-Shen Hsin, Ryohei Kobayashi, Carolyn Zhang SciPost Phys. 20, 006 (2026) · published 13 January 2026 doi: 10.21468/SciPostPhys.20.1.006 pdf BiBTeX RIS Submissions/Reports Abstract 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 $(G,K,\omega_{D+1},\alpha_D)$ in $D$ spacetime dimensions where $G$ is a group and $K\subset G$ is a discrete subgroup, $\omega_{D+1}$ is a $(D+1)$-cocycle for group $G$, and $\alpha_{D}$ 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 $A_5/\Z_2$ symmetry, with realizations in lattice models. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.1.006TI - Anomalies of coset non-invertible symmetriesPY - 2026/01/13UR - https://scipost.org/SciPostPhys.20.1.006JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 1SP - 006A1 - Hsin, Po-ShenAU - Kobayashi, RyoheiAU - Zhang, CarolynAB - 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 $(G,K,\omega_{D+1},\alpha_D)$ in $D$ spacetime dimensions where $G$ is a group and $K\subset G$ is a discrete subgroup, $\omega_{D+1}$ is a $(D+1)$-cocycle for group $G$, and $\alpha_{D}$ 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 $A_5/\Z_2$ symmetry, with realizations in lattice models.ER - × @Article{10.21468/SciPostPhys.20.1.006, title={{Anomalies of coset non-invertible symmetries}}, author={Po-Shen Hsin and Ryohei Kobayashi and Carolyn Zhang}, journal={SciPost Phys.}, volume={20}, pages={006}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.1.006}, url={https://scipost.org/10.21468/SciPostPhys.20.1.006},} Ontology / Topics See full Ontology or Topics database. 't Hooft anomalies Discrete gauge theories Global symmetries Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 Po-Shen Hsin, 2 Ryohei Kobayashi, 3 Carolyn Zhang 1 King's College London [KCL] 2 Institute for Advanced Study [IAS] 3 Harvard University Funders for the research work leading to this publication Simons Foundation Society of Fellows, Harvard University United States Department of Energy [DOE]