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

Vincent Braunack-Mayer, Hisham Sati, Urs Schreiber

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)197-265
Number of pages69
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Oct 1 2019

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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