an article that we are finalizing at CQTS:
Hisham Sati$\;$and$\;$ Urs Schreiber:
Flux Quantization
commissioned for:
Encyclopedia of Mathematical Physics 2nd ed
Elsevier (2024)
download:
pdf (v2)
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 [FSS23Char] 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.
This article parallels the expository Part I (“Flux Quantization”) of the lecture notes:
The main theory underlying the article is laid out in:
Concise exposition of the notions invoked in §3.3 is in:
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Last revised on July 26, 2024 at 14:10:35. See the history of this page for a list of all contributions to it.