Schreiber Engineering of Anyons on M5-Probes

An article that we are finalizing at CQTS:

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

  
  

  Engineering of Anyons on M5-Probes

  via Flux-Quantization

  
  

  part II of: Introduction to Hypothesis H

  
  

  download: [pdf to appear here]

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Abstract: Comprehensive flux-quantization of the M5-brane‘s tensor field – consistent with its non-linear self-duality and with its twisting by the bulk C-field – exists only in little-studied non-abelian generalized cohomology theories, notably in a twisted equivariant (and “twistorial”) form of unstable Cohomotopy (“Hypothesis H”) — but it is only through such flux-quantization that the field is globally completed, with well-defined solitonic configurations and torsion charges.

In these lecture notes we review the construction for an audience familiar with the general notion of flux-quantization (for which see SS24). The key result is a rigorous first-principles derivation of (abelian) anyonic soliton quantum states on (single) magnetized M5-branes probing Seifert orbi-singularities (“geometrc engineering” of anyons), which we motivate from open problems in the field of quantum computing.

Readers are expected to be acquainted with the topic of part I of the lecture notes:

• Flux Quantization

Based on:

• Flux Quantization on M5-Branes

• Anyons on M5-Probes of Seifert 3-Orbifolds