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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Topological Field Theor y on a Lattice, Discrete Theta-Angles and Confinement
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abstract
We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite abelian group (the magnetic gauge group). We show that possible theta-angles in such a theory are quantized and labeled by quadratic functions on the magnetic gauge group. When the theta-angles vanish, the theory is dual to an ordinary topological gauge theory, but in general it is not isomorphic to it. We also explain how to couple a lattice Yang-Mills theory to a TQFT of this kind so that the 't Hooft flux is well-defined, and quantized values of the theta-angles are allowed. The quantized theta-angles include the discrete theta-angles recently identified by Aharony, Seiberg and Tachikawa.
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The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking.
Superconductors are bosonic at low energy yet carry a gravito-magnetic anomaly from fermion parity gauging that forbids trivial massive phases in 3D and 4D.
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.
citing papers explorer
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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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Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation
The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking.
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Gauging in superconductors and other electronic systems
Superconductors are bosonic at low energy yet carry a gravito-magnetic anomaly from fermion parity gauging that forbids trivial massive phases in 3D and 4D.
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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.