Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs

Journal article

We study the anomalies of non-invertible symmetries in 1+1D QFTs using gapped boundaries of its SymTFT. We establish the explicit relation between Lagrangian algebras which determine gapped boundaries of the SymTFT, and algebras which determine non-anomalous/gaugeable topological line operators in the 1+1D QFT. If the Lagrangian algebras in the SymTFT are known, this provides a method to compute algebras in all fusion categories that share the same SymTFT. We find necessary conditions that a line operator in the SymTFT must satisfy for the corresponding line operator in the 1+1D QFT to be non-anomalous. We use this constraint to show that a non-invertible symmetry admits a 1+1D trivially gapped phase if and only if the SymTFT admits a magnetic Lagrangian algebra. We define a process of transporting non-anomalous line operators between fusion categories which share the same SymTFT and apply this method to the three Haagerup fusion categories.

Authors: Putrov, P; Radhakrishnan, R

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of High Energy Physics
• Volume: 2026
• Issue: 3
• Article number: 77
• Publication date: 2026-03-09
• Acceptance date: 2026-01-01
• DOI: 10.1007/jhep03(2026)077
• EISSN: 1029-8479
• ISSN: 1126-6708
• Language: English
• Keywords: Topological Field Theories; Field Theories in Lower Dimensions; Discrete Symmetries; Anomalies in Field and String Theories