Schreiber Non-Lagrangian construction of abelian CS/FQH theory

A couple of talks that I (will) have given:

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• Urs Schreiber$\;\;$ on joint work with $\;\;$ Hisham Sati:

  
  

  Non-Lagrangian construction of
  abelian CS/FQH-theory via
  flux quantization in 2-Cohomotopy

  
  

  talk at:

  • Topology and Geometry Seminar, Texas Tech (26 March 2025)

  • ISQS29, Prague (7-11 July 2025)

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Abstract: After briefly recalling how the analog of Dirac charge quantization in exotic (effective, higher) gauge theories – providing their global topological completion – is encoded in a choice of classifying space $\mathscr{A}$ whose rationalization reflects the flux Bianchi identities, I explain how the choice $\mathscr{A} \coloneqq S^2 \simeq \mathbb{C}P^1 \subset \mathbb{C}P^\infty \simeq B \mathrm{U}(1)$ (“flux quantization in 2-Cohomotopy”) implements effective corrections to ordinary Dirac flux quantization, which over surfaces yields exactly the topological quantum observables of fractional quantum Hall systems, traditionally described by abelian Chern-Simons theory. I close by briefly indicating how this situation is geometrically engineered on probe M5-branes if the M-theory C-field is flux-quantized in 4-Cohomotopy (“Hypothesis H”).

Based on:

• Fractional Quantum Hall Anyons via the Algebraic Topology of exotic Flux Quanta

Related presentations:

• Rethinking Topological Quantum (lightning talk)

• Rethinking FQH Anyons (talk)

• Engineering of Anyons on M5-Probes

• Abelian Anyons on Flux-Quantized M5-branes