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Higher Symmetry and Gapped Phases of Gauge Theories

Part of the Progress in Mathematics book series (PM,volume 324)

Abstract

We study topological field theory describing gapped phases of gauge theories where the gauge symmetry is partially Higgsed and partially confined. The TQFT can be formulated both in the continuum and on the lattice and generalizes Dijkgraaf–Witten theory by replacing a finite group by a finite 2-group. The basic field in this TQFT is a 2-connection on a principal 2-bundle. We classify topological actions for such theories as well as loop and surface observables. When the topological action is trivial, the TQFT is related to a Dijkgraaf–Witten theory by electric-magnetic duality, but in general it is distinct.We propose the existence of new phases of matter protected by higher symmetry.

Mathematics Subject Classification (2010).

  • 79: Mathematical Physics

Keywords

  • Symmetries
  • higher categories
  • topological phases of matter

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Kapustin, A., Thorngren, R. (2017). Higher Symmetry and Gapped Phases of Gauge Theories. In: Auroux, D., Katzarkov, L., Pantev, T., Soibelman, Y., Tschinkel, Y. (eds) Algebra, Geometry, and Physics in the 21st Century. Progress in Mathematics, vol 324. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59939-7_5

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