Flux Quantization
arXiv:2402.18473 · doi:10.1016/B978-0-323-95703-8.00078-1
Abstract
Flux- and charge-quantization laws for higher gauge fields of Maxwell type -- e.g. the common electromagnetic field (the "A-field") but also the B-, RR-, and C-fields considered in string/M-theory -- specify non-perturbative completions of these fields by encoding their solitonic behaviour and hence by specifying the discrete charges carried by the individual branes (higher-dimensional monopoles or solitons) that source the field fluxes. This article surveys the general (rational-)homotopy theoretic understanding of flux- and charge-quantization via the Chern-Dold character map generalized to the non-linear (self-sourcing) Bianchi identities that appear in higher-dimensional supergravity theories, notably for B&RR-fields in D=10, for the C-field in D=11 supergravity, and for the B-field on fivebrane worldvolumes.
34+6 pages, many figures; v2: published version, commissioned for the Encyclopedia of Mathematical Physics 2nd ed
References in corpus (10)
- Fractional M2-branes
- The Uncertainty of Fluxes
- Heisenberg Groups and Noncommutative Fluxes
- On Kottler's path: origin and evolution of the premetric program in gravity and in electrodynamics
- The Rational Higher Structure of M-theory
- Basics of M-Theory
- D-Branes, RR-Fields and Duality on Noncommutative Manifolds
- Higher Gauge Theory
- The action principle and the supersymmetrisation of Chern-Simons terms in eleven-dimensional supergravity
- Classifying A-field and B-field configurations in the presence of D-branes
Cited by in corpus (10)
- Flux Quantization on M5-branes
- Quantum Observables of Quantized Fluxes
- Anyons on M5-Probes of Seifert 3-Orbifolds via Flux Quantization
- The Hidden M-Group
- Engineering of Anyons on M5-Probes via Flux Quantization
- Holographic M-Brane Super-Embeddings
- Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems
- Gauge potentials on the M5 brane in twisted equivariant cohomotopy
- The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces
- Flux Quantization on M-Strings