Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 15th 2009

    created fivebrane 6-group with the idea

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeJan 16th 2022
    If one goes up the Whitehead tower starting from orthogonal group, one passes by the special orthogonal group, the spin group, the string 2-group before finally reaching the fivebrane 6-group. What comes after the fivebrane 6-group?
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 16th 2022
    • (edited Jan 16th 2022)

    By dimensional reasons it’s natural to speculate that killing the next non-torsion homotopy group gives “ninebrane structure” (Sati: arXiv:1405.7686). But there remains little known for sure on the physics side about the would-be nine-brane that one can compare the resulting structure to.

    To some extent this problem was already the case for the fivebrane structures. Just to note in this case that – under “Hypothesis H” – we gave a rigorous proof that fivebrane structure cancels an M5-brane anomaly: see Ex. 3.2 and Rem. 4.3 in “Twisted Cohomotopy implies M5 WZ term level quantization”.

    Since this discussion ultimately rests all on the quaternionic Hopf fibration S 7S 4S^7 \to S^4, it is natural to speculate that a variant based instead on the octonionic Hopf fibration S 15S 7S^{15} \to S^7 would give an analogous rigorous statement about 9-brane structure. But this would remain to be worked out.

    • CommentRowNumber4.
    • CommentAuthorSamuel Adrian Antz
    • CommentTimeJul 4th 2024
    • (edited Jul 4th 2024)

    Is the title of fivebrane 6-group supposed to be small, when that of Fivebrane group is not?

    Edit: I just looked at the pages for ninebrane 10-group and ninebrane group, where both titles are small.

    Edit: string 2-group and string group are also both small.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJul 4th 2024

    never made up my mind on this. The issue starts with “spin group”.

    Let’s agree on a convention and then try to harmonize the entry titles.