  A key open problem in M-theory is the mechanism of "gauge enhancement", which
supposedly makes M-branes exhibit the nonabelian gauge degrees of freedom that
are 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 invariant meaning, the problem is really the lift to M-theory
of the twisted K-theory classification of D-brane charges. Here we show how
this problem has a solution by universal constructions in super homotopy
theory, at least rationally. 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, at the level of rational homotopy theory, that 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.
