Higher symmetry and gapped phases of gauge theories

By A. Kapustin, Ryan Thorngren. 2013

266 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bae004648dc2cd293304ec49c981a660f62c7f48

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Exploring 2-group global symmetries (2018, background): “15) to symmetries was pointed out in [11], where the underlying mathematical structure was identified as a 2-group [12] (see sections 1.”
Universal Non‐Invertible Symmetries (2022, background): “This slightly refines the classification of 2-group SPT phases appearing in [34].”
Coupling a QFT to a TQFT and duality (2014, unknown): “(More general cases were discussed in [11,12].”
Topological phases with generalized global symmetries (2015, background): “…global symmetries Beni Yoshida Walter Burke Institute for Theoretical Physics and Institute for Quantum Information & Matter, California Institute of Technology, Pasadena, California 91125, USA and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106,…”
Generalized global symmetries (2014, background): “The purpose of this paper is to explore the consequences of such global symmetries [10,11] rather than their local gauged versions.”
State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter (2016, background): “ymmetry a7!a+ ; b7!b+ ; ;2Z1(M;Z 2): (B.3) Crucially, F 0 acts on F 1 by a nontrivial automorphism exchanging and . The combined symmetry is described by a 2-group (or equivalently a crossed module) [38]. In general, the equivalence class of a 2-group F is described by a pair of groups F 0;F 1, wher”
Generalized Symmetries in Condensed Matter (2022, unknown): “We can combine the ingredients of the above discussions, and consider SPT phases protected by higher-form symmetries (21).”
On 2-group global symmetries and their anomalies (2018, methodology): “Therefore, as remarked in [8], (2.”
Symmetry protected topological phases and generalized cohomology (2017, background): “ with fermion number symmetry, higher form symmetries, etc., simply by allowing G b to \act" non-trivially on the spectrum GP [Kit13] or by replacing the classifying space BG b with other spaces [KT13]. Part of our analysis applies to the more general problem of endowing some topological phase ”
Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, background): “The cluster state on this lattice is an SPT phase protected by a global Z2 symmetry U = ∏ a∈AXa, as well as a “1-form symmetry”, U γ = ∏ b∈γ⊂B Xb, meaning a symmetry defined for each closed curve γ on the bonds of the square lattice [97, 116, 117].”
Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward (2022, unknown): “In higher dimensions, gauge theories of nil-2 groups naturally generalize to higher group gauge theories [121] where Abelian 0-form symmetries are “centrally” extended by higher-form symmetries.”
Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases (2019, background): “One can apply a similar reasoning to general d space dimensions, but where now since the Wilson lines are codimension d− 1, they generate d− 1-form symmetries [23,32].”
Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions (2016, background): “t. How do we go beyond the twisted gauge theory description of Dijkgraaf-Witten model? Other TQFTs that are beyond Dijkgraaf-Witten model, such as R B IdA I+ B IB J [29,37]and other higher form TQFTs [38], may still be captured by the analogous lattice Hamiltonian model in Eq. (3) by modifying the d”
Comments on abelian Higgs models and persistent order (2017, background): “See [26] for details on these objects and other physical applications.”