q-form global symmetries generalize ordinary symmetries to higher-dimensional charged objects, leading to new rules for amplitudes, gauging, breaking, and anomaly inflow in quantum field theories.
Topological Quantum Field Th eory, Nonlocal Operators, and Gapped Phases of Gauge Theories
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abstract
We revisit the role of loop and surface operators as order parameters for gapped phases of four-dimensional gauge theories. We show that in some cases surface operators are confined, and that this fact can be used to distinguish phases which are not distinguished by the Wilson-'t Hooft criterion. The long-distance behavior of loop and surface operators which are neither confined nor screened is controlled by a 4d TQFT. We construct these TQFTs for phases which are characterized by the presence of electrically and/or magnetically charged condensates. Interestingly, the TQFT describing a phase with a nonabelian monopole condensate is based on the theory of nonabelian gerbes. We also show that in phases with a dyonic condensate the low-energy theta-angle is quantized.
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Field theories with ℤ_N p-form symmetry generically admit a Coulomb phase where the infrared theory is Abelian p-form electrodynamics, illustrated via continuum and lattice examples.
Ground-state expectation values of slow-momentum observables in QFTs can be approximated by averages over the critical fixed-point theories via fidelity-based hyperscaling relations.
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Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.
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Generalized Global Symmetries
q-form global symmetries generalize ordinary symmetries to higher-dimensional charged objects, leading to new rules for amplitudes, gauging, breaking, and anomaly inflow in quantum field theories.
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Discrete $p$-Form Symmetry and Higher Coulomb Phases
Field theories with ℤ_N p-form symmetry generically admit a Coulomb phase where the infrared theory is Abelian p-form electrodynamics, illustrated via continuum and lattice examples.
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Hyperscaling of Fidelity and Operator Estimations in the Critical Manifold
Ground-state expectation values of slow-momentum observables in QFTs can be approximated by averages over the critical fixed-point theories via fidelity-based hyperscaling relations.
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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
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Lectures on Generalized Symmetries
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.