Schreiber StringMath2017

A talk that I have given:

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$\;$ Urs Schreiber (CAS Prague & HCM Bonn)

$\;$ Super $p$-Brane Theory emerging

$\;$ from Super Homotopy Theory

$\;$ talk at String Math 2017, Hamburg $\;\;\;$ (slides, expo, video, YT)

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Abstract. It is a notorious open problem to determine the nature of the non-pertubative theory formerly known as Strings. I present results showing that, rationally, many of its phenomena emerge as stages of a Whitehead tower, invariant modulo R-symmetry, that emerges out of the superpoint regarded in super-geometric rational homotopy theory:

This includes super-spacetime as such, the bouquet of all Green-Schwarz super p-branes, D-brane charge in twisted K-theory, M-brane charge, double dimensional reduction, T-duality, Buscher rules for RR-fields, doubled spacetimes, F-theory fibrations, S-duality. The orbifold $S^4/S^1$ (familiar from the near horizon geometry of M5-branes at A-type singularities) appears in a surprising unifying role.

These results (arXiv:1611.06536, arXiv:1702.01774 and arXiv:1806.01115) are joint with Hisham Sati and Vincent Braunack-Mayer, John Huerta, Domenico Fiorenza, see below.

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For comprehensive review see:

• 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

This anlysis in super-rational homotopy theory led to a hypothesis about its non-rational completion, see at

• Hypothesis H

for more on this.

Further related talks:

• The Higher Structure of 11d Supergravity

  talk at Souriau 2019

  IHP Paris, 2019

• Twisted Cohomotopy implies M-theory anomaly cancellation

  presentation at Strings 2019

  Brussels, 2019

• Equivariant Cohomotopy and Branes

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

  NUS Singapore, 2018

• Equivariant Super Homotopy Theory

  talk at Geometry in Modal Homotopy Type Theory

  CMU Pittsburgh, 2019

• Introduction to Higher Supergeometry

  talk at Higher structures in M-theory, 2018

  Durham, 2018

• Super topological T-Duality

  talk at Duality in Homotopy Theory 2017

  Regensburg, 2017

• Super Lie n-algebra of Super p-branes

  talk at TQFT Seminar Lisbon, 2017 alongside Iberian Strings 2017

  IST Lisbon, 2017

• Structured Homotopy Theory and String Theory

  talk at Geometry, Topology and Physics 2018

  NYU Abu Dhabi, 2018

• Equivariant Stable Cohomotopy and Branes

  talk at Geometry, Topology and Physics 2018

  NYU Abu Dhabi, 2018

Related lecture notes:

• From the Superpoint to T-Folds

• geometry of physics

  • geometry of physics – categories and toposes

  • geometry of physics – fundamental super p-branes

Related articles in the approximation of rational Cohomotopy:

• Super Lie n-algebra extensions, higher WZW models and super p-branes

• The WZW term of the M5-brane

• Rational sphere valued supercocycles in M-theory

• T-Duality from super Lie n-algebra cocycles for super p-branes

• Higher T-duality of super M-branes

• M-Theory from the Superpoint

• Equivariant homotopy and super M-branes

• Gauge enhancement of Super M-Branes

• Super-exceptional embedding construction of the M5-brane

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

Related articles in full twisted/equivariant Cohomotopy (Hypothesis H):

• 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 M5 WZ term level quantization

  arXiv:1906.07417

• Hisham Sati, Urs Schreiber:

  Equivariant Cohomotopy implies orientifold tadpole cancellation

  arXiv:1909.12277

• Hisham Sati, Urs Schreiber,

  Lift of fractional D-brane charge to equivariant Cohomotopy theory

  arXiv:1812.09679

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