M5-branes' flux quantization linked to non-abelian cohomology.
problem Flux quantization on M5-branes and its implications.
method Analogous to Dirac's charge/flux quantization, constraining M5's flux-quantization law to non-abelian cohomology theory.
result Skyrmion-like and anyonic solitons on M5-branes and open M5-branes.
New method for flux quantization on phase space stacks.
problem Defining and constructing flux-quantized phase space stacks.
method Observation of flux densities and characterization of Cauchy data.
result Flux-quantized phase space stacks have classifying spaces with rational Whitehead L-infinity algebra.
11D supergravity completes with quantized C-field flux.
problem Completing 11D supergravity with quantized C-field flux.
method Duality-symmetric formulation of on-shell 11d supergravity on superspace.
result 11d super-spacetimes are quantizable by duality-symmetric super-C-field flux.
Analyzes quantization of flux observables in gauge theories.
problem Lifting Poisson-brackets of flux observables to higher moduli stacks.
method Systematic analysis of canonical quantization and flux quantization laws.
result Topological quantum observables form homology Pontrjagin algebra of loop space.
Modernizes higher-dimensional supergravity, linking it to flux quantization.
problem Constructing infrared completions of higher-dimensional supergravity.
method Using differential nonabelian cohomology and super-torsion constraints.
result Equivalence of solutions in different dimensions and flux quantization.
10D IIA Superspace is put on shell by imposing duality-symmetric Bianchi identities on super-flux densities.
problem Dimensional reduction of 11D supergravity to 10D IIA
method Cyclification of 11D supergravity
result Full 10D IIA supergravity is put on shell with duality-symmetric Bianchi identities.
We develop a Chern character map for twisted equivariant non-abelian cohomology.
problem Understanding non-abelian cohomology theories and their applications.
method General construction of the Chern character map for twisted equivariant non-abelian cohomology.
result Illustrated the construction by computing the equivariant Sullivan model of Cohomotopy.
Higher gauge theory via differential nonabelian cohomology
problem Global infrared completion of higher gauge fields
method Maxwell-type higher gauge fields
result Electromagnetic flux quantization
We consider the hypothesis that the C-field 4-flux and 7-flux forms in M-theory are in the image of the non-abelian Chern character map from the non-abelian generalized cohomology theory called J-twisted Cohomotopy theory. We prove for M2-brane backgrounds in M-theory on 8-manifolds that such charge quantization of the…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological extension of the action and the topological flux quantization conditions, in terms …
The paper explores how fields in higher dimensions are quantized.
problem Understanding non-perturbative completions of higher gauge fields.
method Generalizes the Chern-Dold character map to higher-dimensional supergravity theories.
result Flux and charge quantization laws for higher gauge fields are understood via non-linear Bianchi identities.
We continue our study of a general class of N=2 supersymmetric AdS3×Y7 and AdS2×Y9 solutions of type IIB and D=11 supergravity, respectively. The geometry of the internal spaces is part of a general family of "GK geometries", Y2n+1, n≥3, and here we study examples in which $Y…
We study a variational Ginzburg-Landau type model depending on a small parameter ε>0 for (tangent) vector fields on a 2-dimensional Riemannian manifold S. As ε→0, these vector fields tend to have unit length so they generate singular points, called vortices, of a (non-zero) index if the g…
New mathematical framework connects M-theory charges to stable homotopy groups.
problem Quantization of fluxes in M-theory and their mathematical representation.
method Establishing a correspondence between M-theory phenomena and stable homotopy theory concepts.
result Found a direct link between M-theory charges and stable homotopy groups.
We uncover and highlight relations between the M-branes in M-theory and various topological invariants: the Hopf invariant over Q, Z and Z2, the Kervaire invariant, the f-invariant, and the ν-invariant. This requires either a framing or a corner structure. The canonical framing pro…
Unified super-symmetry and higher fluxes using super-Lie-infinity algebras.
problem Unified extended super-symmetry and higher flux densities.
method Using super-Lie-infinity algebras and their extensions and cyclifications.
result Derivation of topological T-duality laws from super-Lie-infinity structure.