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Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory
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Gauge theories in 2+1 dimensions whose gauge symmetry is spontaneously broken to a finite group enjoy a quantum group symmetry which includes the residual gauge symmetry. This symmetry provides a framework in which fundamental excitations (electric charges) and topological excitations (magnetic fluxes) can be treated on equal footing. In order to study symmetry breaking by both electric and magnetic condensates we develop a theory of symmetry breaking which is applicable to models whose symmetry is described by a quantum group (quasitriangular Hopf algebra). Using this general framework we investigate the symmetry breaking and confinement phenomena which occur in (2+1)-dimensional gauge theories. Confinement of particles is linked to the formation of string-like defects. Symmetry breaking by an electric condensate leads to magnetic confinement and vice-versa. We illustrate the general formalism with examples where the symmetry is broken by electric, magnetic and dyonic condensates.
Forward citations
Cited by 2 Pith papers
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The Classification of 3+1d Symmetry Enriched Topological Order
Finite-group-enriched 3+1d topological orders are classified by 2SVect-enriched G-crossed braided fusion 2-categories, with gauging obstructions living in SW^5(BG).
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Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy II -- Cutting through the boundary
When an entanglement cut ends on a gapped boundary of a 2+1D topological phase, the topological entanglement entropy is controlled by the half-linking matrix, which replaces the modular S matrix used without boundaries.
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