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I notice that in recent preprints (see equation (2.1) in today’s 1108.4060) people are getting awefully close to rediscovering nonabelian 2-connections in the worldvolume theory of NS-fivebranes (but they are forgetting the associator! :-).
This follows a famous old conjecture by Witten, which says that the worldvolume theory of a bunch of fivebranes on top of each other (what physicsist call a “stack” of fivebranes) should be a nonabelian principal 2-bundle/gerbe-gauge theory. If you have followed Witten’s developments since then (with his latest on Khovanov homology) you’ll know that he is suggesting that this theory is at the very heart of a huge cluster of concepts (geometric Langlands duality and S-duality being part of it).
So I should eventually expand the entry fivebrane . I’ll start with some rudiments now, but will have to interrupt soon. Hopefully more later.
Okay, I have added a bit of content to fivebrane
a brief stub section on the nonabelian 2-connection aspect;
a brief section on how Khovanov homology comes in (taken from an old blog post of mine)
references.
I think I’ll interrupt now, write up a section on 2-connections and then email Henning Samtleben…
Do you mean to begin
The F5-brane…
in an entry on NS5-branes? What do these prefix letters mean?
Right, this is a mess. I need to find a quiet moment to work on this entry. Not only that the terminology jumps, but it never actually gives anything close to a definition.
But briefly, the coding goes like this:
not all extended objects are D-branes. For instance the string sigma-model that carries the structure in string perturbation theory is a 1-brane, but not a D-brane. Since it is the “fundamental string” one calls it the “F1-brane”. SImilarly then there is supposed to be 6-dimensional sigma model describing a fundamental 5-brane dynamics and so this is the “F5-brane”.
But it so happens that these perturbative objects re-appear as solitons in the effective background theory: there are charged higher dimensional “black hole”-like solutions in type II supergravity: one that looks like a “black string” the other like a “black 5-brane”. These usually then go by the name “NS string” and “NS fivebrane”. This is because the fields that constitute these solutions (gravity and p-form fields) have as quanta the superstring’s exictations in the “Neveu-Schwarz sector” of the worldsheet theory.
A long story, as you can see. I promise to tell it once. But not right now.
I just noticed that I was violating my own principles here: starting to write explanations on the Forum without doing something on the Lab.
So I took ten minutes and wrote a more substantial Idea-section at fivebrane. Still sketchy, but maybe this now qualifies as an Idea ;-)
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