On the resolution of categorical symmetries in (Non-) Unitary Rational CFTs

arXiv:2511.16363 · hep-th, cond-mat.str-el, math-ph, math.MP, math.QA, quant-ph · Submitted 2025-11-20 · Read on arXiv

hep-th, cond-mat.str-el, math-ph, math.MP, math.QA, quant-ph

Submitted: 2025-11-20

Updated: 2026-09-21

Comments: 49 pages, 2 figures, discussion regarding cloaking boundary and non-diagonal case is updated, accepted for publication in SciPost Physics Core

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Entanglement — 75× in this paper · explained in 3 episodes
• Entanglement Entropy — 24× in this paper · explained in 2 episodes
• Topological Order — 5× in this paper · explained in 2 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Anyons — 2× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Degeneracy — 2× in this paper · explained in 3 episodes
• Topological Defects — 2× in this paper · explained in 2 episodes
• Vertex Operator Algebra — 2× in this paper
• Additivity — 1× in this paper · explained in 1 episode
• Adjacency Matrix — 1× in this paper · explained in 1 episode
• Domain Walls — 1× in this paper · explained in 2 episodes
• Modular flow — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra
• Generalized Global Symmetries
• Generalized Symmetries in Condensed Matter
• On finite symmetries and their gauging in two dimensions
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases
• Non-Invertible Global Symmetries and Completeness of the Spectrum
• Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond
• Non-invertible Global Symmetries in the Standard Model
• Branes and Non-Invertible Symmetries
• Non-Invertible Chiral Symmetry and Exponential Hierarchies
• Non-Invertible Gauss Law and Axions
• Non-invertible Time-reversal Symmetry
• Non-Invertible Symmetries from Holography and Branes
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• ICTP Lectures on (Non-)Invertible Generalized Symmetries
• Generalized Charges, Part I: Invertible Symmetries and Higher Representations
• Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
• Categorical Landau Paradigm for Gapped Phases
• Quantization of Axion-Gauge Couplings and Non-Invertible Higher Symmetries

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