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Anomalies of Coset Non-Invertible Symmetries

by Po-Shen Hsin, Ryohei Kobayashi, Carolyn Zhang

Submission summary

Authors (as registered SciPost users): Po-Shen Hsin · Ryohei Kobayashi
Submission information
Preprint Link: scipost_202503_00040v1  (pdf)
Date submitted: 2025-03-22 06:51
Submitted by: Kobayashi, Ryohei
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Mathematical Physics

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 $A_5/\mathbb{Z}_2$ symmetry, with realizations in lattice models.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing

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