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An Introduction to Higher-Form Symmetries
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abstract
These notes are intended to be a pedagogical introduction to higher-form symmetries, which are symmetries whose charged objects are extended operators supported on lines, surfaces, and etc. This subject has been one of the most popular and effervescent topics of theoretical physics in recent years. Gauge theories are central in the study of higher-form symmetries, with Wilson and 't Hooft operators corresponding to the charged objects. Along these notes, we discuss in detail some basic aspects, including Abelian Maxwell and Chern-Simons theories, and $SU(N)$ non-Abelian gauge theories. We also discuss spontaneous breaking of higher-form symmetries.
Forward citations
Cited by 14 Pith papers
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On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies
Bordism computation for K(Z,3) identifies a new mixed perturbative anomaly in 5D and a new Z2 discrete anomaly in 7D for U(1) 1-form symmetries.
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Non-invertible symmetries in the axiverse, and the imaginary wormholes
Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.
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Notes on (-2)-form symmetries
Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, an...
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Gravitational index, black hole saddle degeneracy, and one-form symmetry
The |G|-fold degeneracy of supersymmetric AdS5 black hole index saddles is fixed by the flux-quantized BF coupling of the bulk one-form symmetry and persists unmodified in the decompactified black-brane limit.
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Effective field theory for dissipative photons from higher-form symmetries
A Schwinger-Keldysh effective action built on spontaneously broken higher-form symmetry gives dissipative Maxwell equations with an entropy current for photons in insulators.
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Higher-form (Quasi)Hydrodynamics from Holography: Deformations and Dualities
Massless and massive higher-form gauge fields in anti-de Sitter space yield a full low-energy map of diffusive, relaxing, and emergent-photon modes governed by double-trace deformations.
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SymTFT for Continuous Symmetries: Non-linear Realizations and Spontaneous Breaking
Continuous-symmetry SymTFTs are extended to non-linear coset realizations and to spontaneous breaking using boundary and corner constructions, recovering CCWZ actions and SSB Ward identities.
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Non-Invertible Selection Rules on Heterotic Non-Abelian Orbifolds
Non-Abelian orbifolds in heterotic string theory produce non-invertible coupling selection rules, since twisted sectors are labeled by conjugacy classes whose products contain multiple classes and yield characteristic...
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SymTFT actions, Condensable algebras and Categorical anomaly resolutions
For Q8 and Rep(Q8), the paper computes condensable algebras, identifies intrinsically gapless SPT phases, and derives fusion-category short exact sequences that resolve categorical anomalies.
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Symmetry, Symmetry Topological Field Theory and von Neumann Algebra
The symmetric-sector von Neumann algebra of a QFT violates additivity or Haag duality exactly when the Lagrangian algebra of its SymTFT contains operators beyond the identity, with a sharper criterion distinguishing t...
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M2-branes, Higher Form Symmetries and 1-Gerbes
A torsion gerbe on the M2-brane worldvolume cancels a mixed higher-form anomaly, breaking U(1) symmetries to discrete subgroups and imposing a worldvolume flux condition.
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Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations
Tensionless p-branes and branes in degenerate-metric spacetimes admit symmetry transformations built from Killing tensors of arbitrary rank, extending string W-symmetries to all brane dimensions.
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Sandwich Construction of Symmetry TFTs for the Centre Symmetries of Chern-Simons, Yang-Mills, and Einstein Gravity
Constructs AKSZ sandwich SymTFTs with stacky target spaces that encode the center symmetries of Chern-Simons, Yang-Mills, and MacDowell-Mansouri gravity.
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Landau theory for lattice higher gauge theory and Kramers-Wannier duality
Lattice higher gauge theories are rewritten as Landau field theories on closed surfaces, yielding a unified phase description and an infrared duality between higher-form Landau theories.
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