Topological defects

Abstract

This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological quantum field theory in arbitrary dimension, and in higher-dimensional quantum field theory with a focus on 4-dimensional quantum electrodynamics.

arXiv comment37 pages, contribution to the Encyclopedia of Mathematical Physics, 2nd Edition; v2: references added

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Cited by in corpus (10)

• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Revisiting the symmetry-resolved entanglement for non-invertible symmetries in $1+1$d conformal field theories
• Non-invertible defects from the Conway SCFT to K3 sigma models I: general results
• Lattice defect networks in 2d Yang-Mills