### 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.

Original language | English (US) |
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Journal | Communications in Mathematical Physics |

DOIs | |

State | Published - Jan 1 2019 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*. https://doi.org/10.1007/s00220-019-03441-4

**Gauge Enhancement of Super M-Branes Via Parametrized Stable Homotopy Theory.** / Braunack-Mayer, Vincent; Sati, Hisham; Schreiber, Urs.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*. https://doi.org/10.1007/s00220-019-03441-4

}

TY - JOUR

T1 - Gauge Enhancement of Super M-Branes Via Parametrized Stable Homotopy Theory

AU - Braunack-Mayer, Vincent

AU - Sati, Hisham

AU - Schreiber, Urs

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85066029697&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066029697&partnerID=8YFLogxK

U2 - 10.1007/s00220-019-03441-4

DO - 10.1007/s00220-019-03441-4

M3 - Article

AN - SCOPUS:85066029697

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -