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

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.

57 pages, various figures, v2: minor corrections, v3: published version

References in corpus (10)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• An $\infty$-categorical approach to $R$-line bundles, $R$-module Thom spectra, and twisted $R$-homology
• Rational sphere valued supercocycles in M-theory and type IIA string theory
• The Rational Higher Structure of M-theory
• Can D-Branes Wrap Nonrepresentable Cycles?
• M-theory from the Superpoint
• Covariant open bosonic string field theory on multiple D-branes in the proper-time gauge
• A Comparison of two Models of Orbispaces

Cited by in corpus (22)

• Equivariant Cohomotopy implies orientifold tadpole cancellation
• Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds
• Twisted Cohomotopy implies level quantization of the full 6d Wess-Zumino term of the M5-brane
• Twisted Cohomotopy implies twisted String structure on M5-branes
• Twisted Cohomotopy implies M5-brane anomaly cancellation
• Real ADE-equivariant (co)homotopy and Super M-branes
• M/F-Theory as Mf-Theory
• Twistorial Cohomotopy implies Green-Schwarz anomaly cancellation
• Super-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5
• Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers
• Lift of fractional D-brane charge to equivariant Cohomotopy theory
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Global Double Field Theory is Higher Kaluza-Klein Theory
• Flux Quantization
• Flux Quantization on 11-dimensional Superspace
• Rational Homotopy Theory
• Flux Quantization on Phase Space
• Cyclification of Orbifolds
• Quantum Observables of Quantized Fluxes
• Strict algebraic models for rational parametrised spectra I
• Mysterious Triality and the Exceptional Symmetry of Loop Spaces
• Flux Quantization on M-Strings