Schreiber Flux Quantization on M-Strings

An article that we are finalizing at CQTS:

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

  
  

  Flux Quantization on M-Strings

  download: pdf (v2), arXiv:2603.14440 hep-th (v1)

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Abstract. The electric Gauss law in 11D SuGra is famously non-linear, whence its flux quantization must be in nonabelian cohomology. We have previously shown that the minimal admissible choice is 4-Cohomotopy, which in the presence of magnetized M5-probes takes its relative twistorial form.

Here we discuss how this situation is further refined in the presence of M-string probes on the M5-worldvolume. Based on the superspace formulation of 11D SuGra, we find the nested Bianchi identities by iterating the superembedding construction for super $p$-branes. The resulting probe brane hierarchy (M1 on magnetized M5 in 11D bulk) turns out to admit flux quantization in a doubly-relative form of twisted Cohomotopy, classified by the factorization of the quaternionic Hopf fibration through the twistor fibration.

The further equivariant refinement of this cohomology theory reduces on A-type singularities to a form of relative Cohomotopy which geometrically engineers Chern-insulator phases on $M5 \cap \mathrm{A}_n$, with the M-string playing the role of gapped nodal lines.

Based on:

• Flux Quantization

• Flux Quantization on Phase Space

• Flux Quantization on 11D Superspace

• Flux Quantization on M5-Branes