Schreiber The Higher Structure of 11d Supergravity

A talk that I gave:

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• Urs Schreiber

  The Higher Structure
  of
  11-dimensional Supergravity,

  talk at

  Souriau 2019

  IHP Paris, May 2019

  
  

  pdf

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Abstract. Souriau‘s work has shown the immense fruitfulness of giving basic concepts in theoretical physics a precise mathematical foundation. This program of mathematical physics has been outstandingly successful throughout the 20th century, ranging from the mathematical formalization of classical gravity (via Riemannian geometry/Cartan geometry) and gauge theory (via Chern-Weil theory/differential cohomology) over perturbative renormalization (Schwartz distribution theory/microlocal analysis) to perturbative string theory (2d conformal field theory on all genera). However, the success story got stuck with the 2nd superstring revolution: The D-branes/M-branes and weak/strong-coupling string dualities that constitute the modern picture of putative “M-theory” (UV-completed 11-dimensional supergravity) have remained mathematical folklore. But it is precisely these non-perturbative effects that, via holographic QCD (intersecting D-brane models) plausibly solve the Millennium Problem of theoretical physics: non-perturbative QCD.

This talk presents recent progress (FSS 19a, FSS 19b, FSS 19c) on identifying mathematical foundations for M-theory in (co-)homotopy theory (aka “ higher structures”).

Based on:

• 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

• Domenico Fiorenza, Hisham Sati, Urs Schreiber:

  Twisted Cohomotopy implies M-theory anomaly cancellation

  arXiv:1904.10207

• Domenico Fiorenza, Hisham Sati, Urs Schreiber:

  Twisted Cohomotopy implies level quantization of the full 6d Wess-Zumino-term of the M5-brane

  arXiv:1906.07417

Related talks:

• 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,

  Singapore 2018

• The rational higher structure of M-theory

  talk at Higher Structures in M-Theory,

  Durham 2018