In short, I don't know if there is a clear answer to your question at this time.

[Schreiberdk]

Hi there PF

My question here is: Is the Bagger-Lambert-Gustavsson action (http://en.wikipedia.org/wiki/Bagger–Lambert–Gustavsson_action) a way of proving the "M-theory as a matrix model: a conjecture" (http://arxiv.org/abs/hep-th/9610043) or is it a different approach? And how far are we from a full discribtion/proof of the M-theory conjecture?

\Schreiber

 

[mitchell porter]

http://arxiv.org/abs/hep-th/9710009" is still the standard explanation for why the BFSS conjecture should work.

BLG is something different, it was a hypothesis to describe M2-branes, that was subsumed by the later http://arxiv.org/abs/0806.1218" .

M(atrix) theory is about D0-branes, and a D0-brane is an M2-brane shrunk to a point, so there really ought to be a connection, but it's beyond me for now.

 

[atyy]

M(atrix) theory is about D0-branes, and a D0-brane is an M2-brane shrunk to a point, so there really ought to be a connection, but it's beyond me for now.

I think http://arxiv.org/abs/1003.2599" tried to look at this.

 

[mitchell porter]

I said

a D0-brane is an M2-brane shrunk to a point

but I'm not so sure now. My naive conception of M(atrix) theory, pending a proper investigation, was as follows: It describes lots of D0-branes. D0-branes have strings between them. So it's really about M2-branes with other M2-branes stretched between them. The strings are M2-branes with one dimension lost, the D0-branes are M2-branes with two dimensions lost, and losing the dimensions has to do with (1) the switch from M-theory to Type IIA (2) working in the infinite momentum frame. But we are using noncommutative geometry, so "dimension" turns into "number of matrices".

edit: What everyone normally says is that D0-branes are "units of momentum" or "Kaluza-Klein modes" in the eleventh dimension. I can cite http://www.sukidog.com/jpierre/strings/mtheory.htm" to support my contention that the D0-brane is a shrunken M2-brane, but I can't seem to find direct support for this in the technical literature. So here's one way to think about the issue: Suppose we think of M-theory in terms of "branes plus supergravity". The question arises - are these d=11 KK modes excitations of space-time itself, or are they M2-branes moving around the d=11 circle, or is there no difference? A similar question arises for D6-branes, which in M-theory also correspond to a geometric configuration of the background space, rather than to an M-brane configuration.

D-branes are sources for strings, and strings are M2-branes, so whatever a D-brane is, M-theoretically, it has to be a source for M2-branes. But since a geometric configuration can have a potential energy, it can be such a source (think of pair production in curved space-time), so this reasoning doesn't resolve the issue.

Looking at section 3 of the paper cited by atyy, I'm not convinced that even the experts know how to think about this correctly:

We saw that the BFSS model - a (0+1)-dimensional U(N) Matrix model on the worldvolume of N D0-branes - describes M-theory in discrete light cone quantization. However, since the D0−branes are momentum modes on the compact 11th dimension, this description of M-theory is not a fundamental one. Instead, as shown by Sen and Seiberg ..., it appears because of the equivalence of the original M-theory with a decoupled theory of D0-branes living in another M-theory. Any fundamental description of M-theory must involve M2-branes instead, but we don’t know how to formulate it.

"Another M-theory" refers to M-theory compactified on a (very small) space-like circle rather than on a light-like circle. M-theory compactified on a space-like circle is the form of M-theory that was originally discovered by Witten, when looking at the behavior of D0-branes in Type IIA string theory at strong coupling. Seiberg relates the lightlike and the spacelike compactifications through a Lorentz boost. He also takes some limits involving momentum and the Planck mass, and maps the sectors of M(atrix) theory onto the sectors of M-theory as derived from Type IIA.

http://physics.stackexchange.com/questions/6424/good-introductory-text-for-matrix-string-theory"