Emergence from the Superpoint - Comments

[Urs Schreiber]

Urs Schreiber submitted a new PF Insights post

Emergence from the Superpoint

Continue reading the Original PF Insights Post.

 

[john baez]

Very nice article. Here are some typos, in case you want to publish it in a book someday:

" It is known as the curvature of the WZW for the Green-Schwarz super 2-brane in 4d." -
it seems there should be some noun after "WZW".

"On a speculative note, observe that the “branching level” 0, 1, and 2 at which the p-branes appear in the brane bouqte" - should be "bouquet".

"already back in that remarkable artice" - should be "article".

 

[Urs Schreiber]

Thanks! Fixed now.

 

[john baez]

In what sense does the brane bouquet "end" at the point where story ends? Does it end because people haven't explored it further? If so, exploring it further might reveal further treasures! Or does it end for some clear mathematical reason? I often hear people speak of 11-dimensional supergravity as the highest-dimensional supergravity theory that doesn't contain fields of spin > 2. But I've never been very happy with that, since the rationale seems to be that fields of spin > 2 aren't renormalizable... yet nobody has fully settled the issues of renormalizability for various supergravity theories: people seem to keep discovering unexpected cancellations. If the "ending" of the brane bouquet is defined by the requirement of no spins > 2, it would be at least mathematically interesting to drop that requirement and see what comes next - maybe some hidden treasure?

On a vaguely related note, I hear some physicists are getting interested in higher-spin fields; in fact there will be a workshop on them in Singapore:

http://www.ntu.edu.sg/ias/upcomingevents/HSGT/

But I don't know anything about this.

 

[Urs Schreiber]

Right, the bouquet might not end there. I don't presently know if and how it continues. But that's related to the speculative remark I made above, observing that for low values the branching level of the brane bouquet matches the level decomposition of the fundamental representation of E11 (http://ncatlab.org/nlab/show/E11#FundamentalRepresentationAndBraneCharges):
for level 0 (spacetime), level 1 (M2-branes) and 2 (M5-branes). Should that be more than a coincidence, then it might point to the existence of a further 10-cocycle on the M5-brane super Lie 6-algebra corresponding to the "dual graviton" since that is what sits at level 3 in the E11 story.

 

[Urs Schreiber]

Regarding higher spin gauge theory, what I find curious is that this connects to another old appearance of L-infinity algebras in string theory that sometimes seems not to get due attention. Namely first of all, higher spin gauge theory is expected to be the tensionless limit of bosonic string field theory (http://ncatlab.org/nlab/show/higher+spin+gauge+theory#ReferencesRelationToStringTheory). But, second, Zwiebach's seminal work from the 1990 (http://ncatlab.org/nlab/show/string+field+theory#ReferencesHomotopyAlgebra) shows that the genus-0 n-point functions of closed bosonic strings form an L-infinity algebra, even before passing to the tensionless limit. (Hence as the tension does go to zero one should expect, up to some technical subtleties, a kind of contraction limit that takes this tensionful string field L-infinity algebra to a higher spin gauge theory.)

 

[Urs Schreiber]

We now finally have an article on the topic of "Emergence from the superpoint" on the arXiv:

John Huerta and Urs Schreiber:
"M-Theory from the superpoint"
arxiv.org/abs/1702.01774
ncatlab.org/schreiber/show/M-Theory+from+the+Superpoint

Abstract: The "brane scan" classifies consistent Green--Schwarz strings and membranes in terms of the invariant cocycles on super-Minkowski spacetimes. The "brane bouquet" generalizes this by consecutively forming the invariant higher central extensions induced by these cocycles, which yields the complete brane content of string/M-theory, including the D-branes and the M5-brane, as well as the various duality relations between these. This raises the question whether the super-Minkowski spacetimes themselves arise as maximal invariant central extensions. Here we prove that they do. Starting from the simplest possible super-Minkowski spacetime, the superpoint, which has no Lorentz structure and no spinorial structure, we give a systematic process of consecutive maximal invariant central extensions, and show that it discovers the super-Minkowski spacetimes that contain superstrings, culminating in the 10- and 11-dimensional super-Minkowski spacetimes of string/M-theory and leading directly to the brane bouquet.