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Higher Gauge Theory
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This is an invited survey article on higher gauge theory for the Encyclopedia of Mathematical Physics, 2nd edition. In particular, we provide a lightning introduction to higher structures and to the construction of the kinematical data of higher gauge theories, i.e. connections on higher principal bundles. We also summarise the most important applications and dynamical principles that have appeared in the literature, and we close with comments on related areas.
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Cited by 8 Pith papers
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Torsion parallel spinors on Lorentzian four-manifolds and supersymmetric evolution flows on bundle gerbes
Irreducible differential spinors on Lorentzian four-manifolds are reformulated via parabolic pairs and isotropic parallelisms, yielding characterizations of torsion parallel spinors, supersymmetric NS-NS solutions, an...
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Adjusting Higher Chern-Simons Theory
The authors introduce half-adjusted higher Chern-Simons theories, obtained by a cotangent completion of adjusted L8-algebras, which admit consistent gauge transformations and equations of motion implying full flatness.
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Generalized forms of types N = 1, 2 and higher gauge theory
Strict 2- and 3-gauge theory is re-expressed in a single generalized-form formalism in which higher connections, curvatures, Bianchi identities, and gauge transformations match ordinary gauge-theory form, yielding uni...
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Discrete Approximations to $\operatorname{U}(1)$ Principal Bundles in Abelian Gauge Theory
A new discretized Abelian gauge theory T_k is constructed so that as k→∞ it recovers the monopoleless sector of Maxwell theory, unlike naive Z_k gauge theory, which becomes flat Maxwell theory.
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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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Gauged Extended Field Theory and Generalised Cartan Geometry
A systematic Cartan-geometric construction of linearised torsion and curvature hierarchies for generalised geometries with global duality group G and local gauge group H, realised via brane current algebras.
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Higher Gauge Theory via Differential Nonabelian Cohomology
Higher gauge fields receive a global infrared completion by electromagnetic flux quantization in differential nonabelian cohomology using cohesive homotopy theory, with applications to brane charges in K-theory and Co...
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Higher Superspace Supergravity and its IR-Completions
11D supergravity, its toroidal reductions, and M5-brane worldvolume flux are equivalent to Bianchi identities in characteristic L∞-algebras (lS4, cyc(lS4), tor(lS4), lS4S7), whose IR completions are classified by flux...
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