Notes on generalized global symmetries in QFT

By E. Sharpe. 2015

164 citations recorded by the source corpus.

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.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/4fe89028a2d64f4790c2706a6cb7985e2f961d70

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Citations in the corpus

On finite symmetries and their gauging in two dimensions (2017, background): “[4], and one might want to unify the two approaches.”
Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond (2022, background): “For comments on the d = 2 case see for instance [25].”
On 2-group global symmetries and their anomalies (2018, background): “3) Reference [17] also describes some aspects of continuous 1-form symmetry and 2-group symmetry in two spacetime dimensions.”
On gauging finite subgroups (2017, background): “An appearance of higher groups in physics was also noted in [3].”
Generalized Symmetries in Condensed Matter (2022, unknown): “This case is studied in (13, 14, 15) and more generally in (101, 134, 135).”