Schreiber Flux Quantization

an article that we have written at CQTS:

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• Hisham Sati$\;$and$\;$ Urs Schreiber:

  
  

  Flux Quantization

  
  

  commissioned for:

  Encyclopedia of Mathematical Physics 2nd ed

  Volume 4, Elsevier (2025) 281-324

  
  

  doi:10.1016/B978-0-323-95703-8.00078-1

  ISBN:9780323957038

  
  

  download:

  • pdf$\;$(some more typos fixed)

  • arXiv:2402.18473

  
  

  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:

• Introduction to Hypothesis H.

The main theory underlying the article is laid out in:

• The Character Map in Non-Abelian Cohomology

• Flux Quantization on Phase Space

• Flux Quantization on 11d Superspace

• Flux Quantization on M5-Branes

• Flux Quantization on Holographic M5-Branes

Concise exposition of the notions invoked in §3.3 is in:

• Higher Topos Theory in Physics

Related articles.

• Super-Flux Quantization of 11d Supergravity