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 behavior 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.
| Original language | English (US) |
|---|---|
| Title of host publication | Encyclopedia of Mathematical Physics, Second Edition |
| Subtitle of host publication | Volumes 1-5 |
| Publisher | Elsevier |
| Pages | V4:281-V4:324 |
| Volume | 1-5 |
| ISBN (Electronic) | 9780323957069 |
| ISBN (Print) | 9780323957038 |
| DOIs | |
| State | Published - Jan 1 2024 |
Keywords
- Branes
- Charge quantization
- Chern-Dold character
- de Rham cohomology
- Differential cohomology
- Duality
- Electromagnetism
- Flux quantization
- Generalized cohomology
- Higher gauge theory
- Homotopy Lie algebras
- Homotopy theory
- K-theory
- L-infinity algebras
- M-theory
- Monopoles
- Rational homotopy theory
- Solitons
- String theory
- Supergravity
- Twisted cohomology
ASJC Scopus subject areas
- General Mathematics