Schreiber Twisted Cohomotopy implies twisted String structure on M5-branes

An article that we have written:

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• Domenico Fiorenza, Hisham Sati, Urs Schreiber:

  
  

  Twisted cohomotopy implies twisted String structure on M5-branes

  
  

  Journal of Mathematical Physics

  62 (2021) 042301

  
  

  download:

  • pdf (updated)

  • arXiv:2002.11093

  • doi:10.1063/5.0037786

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Abstract. We show that charge-quantization of the M-theory C-field in J-twisted Cohomotopy theory (Hypothesis H) implies emergence of a higher Sp(1)-gauge field on single heterotic M5-branes, which exhibits worldvolume twisted string structure.

(this homotopy-commutative diagram became the logo of M-Theory and Mathematics 2023)

Errata

• In the expression for $2 \widetilde \Gamma_7$ on the first and last page the term “$\widetilde \Gamma + \tfrac{1}{2}p_1$” should read just “$\widetilde \Gamma_4$”.

  (There are two alternative ways of defining $\widetilde \Gamma$ as $\tfrac{1}{2}\chi \pm \tfrac{1}{4}p_1$, which differ by that summand $\tfrac{1}{2}p_1$. But with the convention that we ended up using on p. 4, this conversion summand is absent.)

Followups:

• David Michael Roberts:

  Topological sectors for heterotic M5-brane charges under Hypothesis H, J. High Energ. Phys. 2020, 52 (2020) (arXiv:2003.09832, doi:10.1007/JHEP06(2020)052)

• Domenico Fiorenza, Hisham Sati, Urs Schreiber

  Super-exceptional M5-brane model – Emergence of SU(2)-flavor sector

Exposition and talk notes on Hypothesis H:

• Microscopic Brane Physics from Cohomotopy

  talk at M-Theory and Mathematics

  NYU AD 2020

• Twisted Cohomotopy implies M-theory anomaly cancellation

  presentation at Strings2019

  Brussels, 2019

• Super p-Brane Theory emerging from Super Homotopy Theory

  talk at StringMath2017,

  Hamburg, 2017

• Equivariant Cohomotopy and Branes

  talk at String and M-Theory: The New Geometry of the 21st Century

  NUS Singapore, 2018

• The Higher Structure of 11d Supergravity

  talk at Souriau 2019

  IHP Paris, 2019

• Equivariant Cohomotopy of toroidal orbifolds

  talk at Prof. Sadok Kallel‘s group seminar

  AUS Sharjah, 2019

• Equivariant Stable Cohomotopy and Branes

  talk at Geometry, Topology and Physics

  NYU Abu Dhabi, 2018

• Equivariant cohomology of M2/M5-branes

  talk at Seminar on Higher Structures

  MPI Bonn, 2016

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• Hisham Sati, Urs Schreiber:

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