4.4 Article

Field theories with higher-group symmetry from composite currents

期刊

JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 4, 页码 -

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SPRINGER
DOI: 10.1007/JHEP04(2021)045

关键词

Global Symmetries; Effective Field Theories; Anomalies in Field and String Theories

资金

  1. ToppForsk-UiS program of the University of Stavanger [PR-10614]

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Higher-form symmetries act on extended objects, not on point particles, and can coexist with ordinary point-particle symmetries in a direct product symmetry group. When these symmetries become entangled, a more general mathematical structure related to higher categorical groups is required. Higher-group symmetry can emerge from a bottom-up perspective when physical systems contain at least two different spontaneously broken symmetries.
Higher-form symmetries are associated with transformations that only act on extended objects, not on point particles. Typically, higher-form symmetries live alongside ordinary, point-particle (0-form), symmetries and they can be jointly described in terms of a direct product symmetry group. However, when the actions of 0-form and higher-form symmetries become entangled, a more general mathematical structure is required, related to higher categorical groups. Systems with continuous higher-group symmetry were previously constructed in a top-down manner, descending from quantum field theories with a specific mixed 't Hooft anomaly. I show that higher-group symmetry also naturally emerges from a bottom-up, low-energy perspective, when the physical system at hand contains at least two different given, spontaneously broken symmetries. This leads generically to a hierarchy of emergent higher-form symmetries, corresponding to the Grassmann algebra of topological currents of the theory, with an underlying higher-group structure. Examples of physical systems featuring such higher-group symmetry include superfluid mixtures and variants of axion electrodynamics.

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