Schreiber Exposition of Higher Gauge Theory

An article that we are developing at CQTS:

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

  
  

  Higher Gauge Theory via Differential Nonabelian Cohomology

  
  

  commissioned for:

  Fundamental Structures in Computational and Pure Mathematics,

  Trends in Mathematics, Birkhäuser

  
  

  download:

  • manuscript: pdf, arXiv:2606.12534 (47+10 pages)

  • previous draft: pdf

  
  

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Abstract. An introduction to the global (infrared) completion of Maxwell-type higher gauge fields (as in the higher gauge sectors of higher-dimensional supergravity and its super $p$-branes) by electromagnetic flux quantization in differential nonabelian cohomology, using methods of cohesive homotopy theory. Examples include D/NS brane charge in (unstable) K-theory, M-brane charge in unstable Cohomotopy and geometric engineering of topological quantum order on probe M5-branes.

Related expositions.

• Two Notions of Nonabelian Differential Cohomology

• Higher Topos Theory in Physics

• Flux Quantization

• Globalizing Parallel 2-Transport