Gauge enhancement of super M-branes via parametrized stable homotopy theory

TL;DR

This paper proposes a rational homotopy theory framework to understand gauge enhancement in M-theory, connecting D-brane charge classification to M-brane charges through super homotopy theory and cyclification techniques.

Contribution

It introduces a universal super homotopy theory approach to lift twisted K-theory classifications of D-brane charges to M-brane charges rationally.

Findings

Gauge enhancement explained via lifting in super homotopy theory.

D6 and D8 brane cocycles lifted from twisted K-theory to M-brane cohomology.

Rational homotopy theory provides a new perspective on M-theory gauge phenomena.

Abstract

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.