Schreiber ICMMP26

A talk that I will have given:

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• Urs Schreiber$\;\;$ on work at CQTS with H. Sati:

  
  

  Electromagnetic Flux Quantization
  — IR-Completion of Higher Gauge Fields

  slides: [to appear here]

• keynote talk at ICMMP 2026 (flyer: pdf)

  Session 1: Quantum Field Theory, String and Brane Theory, and Gravitation

  30 Oct – 3 Nov 2026, Hangzhou

  
  

  Abstract: Approaching the centennial of Dirac’s understanding of magnetic flux quantization, the time has come to establish full electromagnetic flux quantization, globally completing higher gauge theories such as higher dimensional supergravities. Beyond conjectural RR-flux quantization in K-theory, this concerns the completion of 11D supergravity and its M-brane probes, with experimentally relevant applications to the geometric engineering of anyonic topological order in fractional quantum Hall systems.
  
  Concretely, since electric Gauss laws are typically non-linear, due to (external or self-sourced) currents, their quantization generally falls outside of traditional Whitehead-generalized cohomology theories and instead requires novel methods of nonabelian cohomology [doi:10.1142/13422]. Previously elusive effects, such as the half-integral shift of the C-field flux in 11D supergravity, now find a natural explanation [doi:10.1007/s00220-020-03707-2].
  
  Applying this understanding to M2/M5-brane probes on A-type orbi-singularities reveals previously unrecognized global topological effects in the self-dual higher gauge field on the M5-brane. These results turn out to admit a fine-grained geometric engineering, now on properly flux-quantized M5-branes, of anyonic topological order as experimentally seen in FQH systems. In particular, this construction predicts that nonabelian anyons, much anticipated in quantum materials research for future topological quantum computing hardware, may be attached to superconducting islands inside FQH liquids.

Based on:

• Flux Quantization (in 11D SuGra, on M5-branes, on M-strings, …)

• Complete Topological Quantization (of 5d MCS, …)

• Higher Superspace Supergravity and its IR-Completions

• Higher Gauge Theory via Differential Nonabelian Cohomology

• Engineering of Anyons on M5-Probes via Flux-Quantization (with SC islands, with boundaries, …)

Related talks:

• Rethinking Topological Quantum

• The $1 Million Puzzle: Hadrons and Quantum Computers