1:05 PM
Regarding the nLab entry on higher spin field theory (ncatlab.org/nlab/show/higher+spin+gauge+theory): It's a stub waiting for some kind soul to take the time to fill in some substance. But as per the above request, I now gone ahead and added some brief lines on the general perspective to the idea-section:
Generally by a higher spin field theory is meant a quantum field theory that involves fields of spin >2 (recalling that a spinor field has spin 1/2, a gauge field has spin 1, a gravitino field has spin 3/2 and the field of gravity has spin 2).
Folklore had it that all massless higher spin field theories are inconsistent due to negative norm states (“ghost”) appearing in their quantization. (This argument underlies the dominance of 𝒩=1 11-dimensional supergravity, see the introduction to the entry 12-dimensional supergravity for more on this https://ncatlab.org/nlab/show/12-dimensional+sup…
Folklore had it that all massless higher spin field theories are inconsistent due to negative norm states (“ghost”) appearing in their quantization. (This argument underlies the dominance of 𝒩=1 11-dimensional supergravity, see the introduction to the entry 12-dimensional supergravity for more on this https://ncatlab.org/nlab/show/12-dimensional+sup…
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1:28 PM
2 hours later…
@ArunDebray thanks, but nothing to be wow-ed by, it's not even an "article" yet. It's just a few sentences as I would say them to you over coffee, to express a broad idea. This entry, like may others, is just a glorified list of references that I found useful to compile. Somebody should eventually fill in some genuine content.
4:18 PM
Good. Yes, it is a beautiful theory, it seems (haven't really worked on it, just had people talk to me about it). I just wish people would go and flesh out the relation to string field theory more (Vasiliev higher spin theory is supposed to be "just" the limit of string field theory as the string tension is taken to zero).
Recently some string folks got excited about the "huge gauge groups" they found in Vasiliev higher spin theory, but that excitement seems a little odd if one remembers that relation to string field theory,
3 hours later…
7:22 PM
8:09 PM
@ArunDebray That closed string field theory is really an L-infinity Chern-Simons theory (see here: ncatlab.org/nlab/show/string+field+theory#AsAnInfinityCSTheory) is not something that seems easy to guess without computation. The actual computation is the great achievement of Barton Zwiebach arxiv.org/abs/hep-th/9206084 .
Curiously, it was only in the process of Zwiebach's work that L-infinity algebras were discovered in the first place!
Traditionally people attribute the idea of L-infinity algebras to Stasheff-Schlessinger 85(ncatlab.org/nlab/show/deformation+theory#SchlessingerStasheff85) but while thatr article does talk about many things differential-graded, it does not talk about L-infinity algebras directly.
Stasheff "admits" on slide 25 here ncatlab.org/nlab/files/StasheffHomotopyStructuresReview.pdf that he really recognized L-infinity in Zwiebach's work.
on string field theory. I guess when he saw it he realized that he could have/should have introduced this evident variant of his then already long established A-infinity algebras, but he didn't. It was Zwiebach who discovered it in string field theory.
But actually, in theiy dual, CE-incarnation, L-infinity algebras were discovered by the Italian supergravity theorists a decade earlier. The concept has a convoluted history: ncatlab.org/nlab/show/L-infinity-algebra#History
Later it was found that open string field theory gives A-infinity structure, and open/closed string field theory combines L-infinity with A-infinity in a way that is tantalizingly close to an "infinity-Lie-Rinehart pair" (ncatlab.org/nlab/show/…), except that one of the axioms of Lie-Rinehart seems to remain unchecked for string field theory, which is a pity or a puzzle.
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