Schreiber Twisted Cohomotopy implies M5 WZ term level quantization

An article that we have written:

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• Domenico Fiorenza, Hisham Sati, Urs Schreiber:

  
  

  Twisted Cohomotopy implies level quantization

  of the full 6d Wess-Zumino-term of the M5-brane

  
  

  Comm. Math. Phys. 384 403–432 (2021)

  
  

  download article:

  • pdf (typos fixed)

  • arXiv:1906.07417

  • doi:10.1007/s00220-021-03951-0

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Abstract. The full 6d Hopf-Wess-Zumino-term in the action functional for the M5-brane is anomalous as traditionally defined. What has been missing is a condition implying the higher analogue of level quantization familiar from the 2d Wess-Zumino term. We prove that the anomaly cancellation condition is implied by “Hypothesis H”: the proposal that the C-field is charge-quantized in twisted Cohomotopy theory. The proof follows by a twisted/parametrized generalization of the Hopf invariant, after identifying the full 6d Wess-Zumino-term with a twisted homotopy Whitehead integral formula, which we establish.

Errata

• In equation (51) here the second “$G_4$” needs to be a “$G_7$”.

Based on

• Domenico Fiorenza, Hisham Sati, Urs Schreiber:

  Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds

  arXiv:1904.10207

• Domenico Fiorenza, Hisham Sati, Urs Schreiber:

  The rational higher structure of M-theory

  Proceedings of the LMS-EPSRC Durham Symposium:

  Higher Structures in M-Theory, August 2018,

  Fortschritte der Physik, 2019

  doi:10.1002/prop.201910017

  arXiv:1903.02834

Followups (Hypothesis H)

• Hisham Sati, Urs Schreiber:

  Equivariant Cohomotopy implies orientifold tadpole cancellation

  (arXiv:1909.12277)

• Hisham Sati, Urs Schreiber,

  Differential Cohomotopy implies intersecting brane observables

  arXiv:1912.10425

• Hisham Sati, Urs Schreiber,

  Twisted Cohomotopy implies M5-brane anomaly cancellation

  arXiv:2002.07737

• Hisham Sati, Urs Schreiber:

  Twisted Cohomotopy implies M5-brane anomaly cancellation

  arXiv:2002.07737

• Domenico Fiorenza, Hisham Sati, Urs Schreiber:

  Twisted Cohomotopy implies twisted String structure on M5-branes

  arXiv:2002.11093

• Domenico Fiorenza, Hisham Sati, Urs Schreiber:

  Twistorial Cohomotopy implies Green-Schwarz anomaly cancellation

  arXiv:2008.08544

• Domenico Fiorenza, Hisham Sati, Urs Schreiber:

  The Character Map in Twisted Non-Abelian Cohomology

  arXiv:2009.11909

• Grigorios Giotopoulos, Hisham Sati, Urs Schreiber:

  Flux Quantization on M5-Branes