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Appears in collection : 2024 IHES Summer School – Symmetries and Anomalies : a Modern Take

I will review aspects of non-invertible symmetries and their relations to anomalies in lattice and continuum field theories. Examples include the Kramers-Wannier symmetry in the quantum Ising lattice model, and the non-invertible chiral symmetry in the 3+1 QED.

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