2024/05/07 by Pavel Putrov, Putrov, Pavel, Rajath Radhakrishnan +1 · 3 citations
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Atomic and Subatomic Physics Research #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Quantum Mechanics and Non-Hermitian Physics #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2405.04619
openalex publication_date 2024/05/07 · openalex created_date 2024/05/11 · openalex updated_date 2026/07/28
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.