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Journal of High Energy Physics

, 2015:172 | Cite as

Generalized global symmetries

  • Davide Gaiotto
  • Anton KapustinEmail author
  • Nathan Seiberg
  • Brian Willett
Open Access
Regular Article - Theoretical Physics

Abstract

A q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have q spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries (q = 0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a sub-group). They can also have ’t Hooft anomalies, which prevent us from gauging them, but lead to ’t Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.

Keywords

Global Symmetries Wilson ’t Hooft and Polyakov loops Topological States of Matter Anomalies in Field and String Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Davide Gaiotto
    • 1
  • Anton Kapustin
    • 2
    Email author
  • Nathan Seiberg
    • 3
  • Brian Willett
    • 3
  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Simons Center for Geometry and PhysicsState University of New YorkStony BrookU.S.A.
  3. 3.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.

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