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Communications in Mathematical Physics

, Volume 371, Issue 1, pp 197–265 | Cite as

Gauge Enhancement of Super M-Branes Via Parametrized Stable Homotopy Theory

  • Vincent Braunack-Mayer
  • Hisham Sati
  • Urs SchreiberEmail author
Article
First Online:

Abstract

A key open problem in M-theory is to explain the mechanism of “gauge enhancement” through which M-branes exhibit the nonabelian gauge degrees of freedom seen perturbatively in the limit of 10d string theory. In fact, since only the twisted K-theory classes represented by nonabelian Chan–Paton gauge fields on D-branes have an invariant meaning, the problem is really the understanding the M-theory lift of the classification of D-brane charges by twisted K-theory. Here we show that this problem has a solution by universal constructions in rational super homotopy theory. We recall how double dimensional reduction of super M-brane charges is described by the cyclification adjunction applied to the 4-sphere, and how M-theory degrees of freedom hidden at ADE singularities are induced by the suspended Hopf action on the 4-sphere. Combining these, we demonstrate that, in the approximation of rational homotopy theory, gauge enhancement in M-theory is exhibited by lifting against the fiberwise stabilization of the unit of this cyclification adjunction on the A-type orbispace of the 4-sphere. This explains how the fundamental D6 and D8 brane cocycles can be lifted from twisted K-theory to a cohomology theory for M-brane charge, at least rationally.

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Notes

Acknowledgements

We are grateful to Augustí Roig and Martintxo Saralegi-Aranguren for discussion of [RS00], as well as to David Corfield, Ted Erler, Domenico Fiorenza, and David Roberts for useful comments. We also thank the anonymous referee for their careful reading and helpful suggestions. VBM acknowledges partial support of SNF Grant No. 200020_172498/1. This research was partly supported by the NCCR SwissMAP, funded by the Swiss National Science Foundation, and by the COST Action MP1405 QSPACE, supported by COST (European Cooperation in Science and Technology).

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HamburgHamburgGermany
  2. 2.Division of Science and MathematicsNew York UniversityAbu DhabiUAE

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