Bootstrapping Non-Invertible Symmetries

Abstract

Using the numerical modular bootstrap, we constrain the space of 1+1d CFTs with a finite non-invertible global symmetry described by a fusion category $\mathcal{C}$. We derive universal and rigorous upper bounds on the lightest $\mathcal{C}$-preserving scalar local operator for fusion categories such as the Ising and Fibonacci categories. These numerical bounds constrain the possible robust gapless phases protected by a non-invertible global symmetry, which commonly arise from microscopic lattice models such as the anyonic chains. We also derive bounds on the lightest $\mathcal{C}$-violating local operator. Our bootstrap equations naturally arise from a "slab construction", where the CFT is coupled to the 2+1d Turaev-Viro TQFT, also known as the Symmetry TFT.

28 pages + references

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Cited by in corpus (18)

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• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
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• Generalized Charges, Part I: Invertible Symmetries and Higher Representations
• Gapped Phases with Non-Invertible Symmetries: (1+1)d
• Subsystem Non-Invertible Symmetry Operators and Defects
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• New Developments in the Numerical Conformal Bootstrap
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal Field Theory
• The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
• TQFT gravity and ensemble holography
• Additivity, Haag duality, and non-invertible symmetries
• Conformal Bootstrap with Duality-Inspired Fusion Rule