Explicit lattice constructions of gauging interfaces and condensation defects are given for higher-dimensional systems with higher-form symmetries, using movement operators to manage constrained Hilbert spaces.
Notes on generalized global symmetries in QFT
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abstract
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as special cases of more general 2-groups and higher groups, and discuss examples of quantum field theories admitting actions of more general higher groups than merely one-form and higher-form symmetries. We discuss analogues of topological defects for some of these higher symmetry groups, relating some of them to ordinary topological defects. We also discuss topological defects in cases in which the moduli `space' (technically, a stack) admits an action of a higher symmetry group. Finally, we outline a proposal for how certain anomalies might potentially be understood as describing a transmutation of an ordinary group symmetry of the classical theory into a 2-group or higher group symmetry of the quantum theory, which we link to WZW models and bosonization.
years
2026 4verdicts
UNVERDICTED 4representative citing papers
Derives Schwinger-Dyson equations and Ward identities in NN-FT to study anomalies in QFTs via a conserved parameter-space current, yielding a new perspective on symmetries.
Half-spacetime gauging of 2-group symmetries in (2+1)d QFTs produces non-invertible duality defects whose fusion rules are derived explicitly from parent theories with mixed anomalies.
In G-theory motivated Type IIB compactifications with varying fields, End of the World branes trivialize a cohomology class and additional non-perturbative objects are required to cancel the bordism group while retaining the class as a subgroup.
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Lattice Gauging Interfaces and Noninvertible Defects in Higher Dimensions
Explicit lattice constructions of gauging interfaces and condensation defects are given for higher-dimensional systems with higher-form symmetries, using movement operators to manage constrained Hilbert spaces.
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Anomalies in Neural Network Field Theory
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Double fibration in G-theory and the cobordism conjecture
In G-theory motivated Type IIB compactifications with varying fields, End of the World branes trivialize a cohomology class and additional non-perturbative objects are required to cancel the bordism group while retaining the class as a subgroup.