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Jena lectures on generalized global symmetries: principles and applications
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This is an elementary set of lectures on generalized global symmetries originally given at the Jena TPI School on QFT and Holography, designed to be accessible to the reader with a basic knowledge of quantum field theory. Topics covered include an introduction to higher-form symmetries with selected applications: Abelian and non-Abelian gauge theories in the continuum and on the lattice, statistical mechanical systems, the Adler-Bell-Jackiw anomaly from the point of view of non-invertible symmetry, and magnetohydrodynamics. Mathematical formalism is kept to a minimum and an emphasis is placed on understanding the global symmetry structure present in well-known models.
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Cited by 8 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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Symmetry TFTs for Continuous Spacetime Symmetries
Continuous spacetime symmetries can be encoded in a (d+1)-dimensional BF/Chern-Simons topological field theory, whose boundary reproduces symmetry generators, symmetry breaking, and anomalies.
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Tilts from 2-Groups
Line operators charged under the 1-form part of a 2-group symmetry must generically break the 0-form part, enforced by a family anomaly derived from Wess-Zumino consistency.
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Perusing confining pseudoreal theories: a story of emerging massless spin-1 bosons
Confining pseudoreal gauge theories leave free massless spin-1 composites in the IR—one for almost all one-species models, two plus an NGB for the only confining two-species model.
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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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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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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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