This is a comment to Lubos' article
on deconstruction. As it got quite long and I would really like to have an answer, I post it here as well:
Maybe this is the right place to ask a question about deconstruction that I have had for quite some time: IIRC, deconstruction (at least for the 6D (2,0) theory relevant for M5 and NS5 branes) starts by looking at D3 branes in a A_N orbifold
which can be written as C^2/Z_N. This gives you the A_N quiver theory.
Then you take a limit in which you take N to infinity while moving away from the orbifold sigularity. The resulting formulas look to me pretty much like you modded out Z from C^2 to end up with a cylinder R^3 x S^1.
Furthermore, what used to be the quiver theory looks like Wati Taylor's version of T-duality in M(atrix) (or any other D-brane gauge theory. In the classic
he describes how you grow an extra dimension from a "SU(N x inifinity)" theory. This should give you a D4 in IIA and you
can apply the usual M-Magic to turn it into a M5 or NS5. So what is more in deconstruction that M(atrix)-T-duality?
Some people I asked this have suggested that the advantage is that you express everything in terms of a renormalizable 4D theory. But this is strictly true only for finite N.
If that were the case you could look at any 6D theory and compactify it on a 2 torus of finite size. You fourier decompose all fields in the compact direction. The fourier components are formally fields in 4D and thus have renormalizable couplings (for a gauge theory say). Of course, non-renormalizabiity comes back when you realize that you have an infinite number of component fields and the sum over all the components will diverge.
Note that I am not trying to argue that all large N limits are ill defined (that would be stupid), I just say that the argument as I understand it sounds too simple to me.
PS: blogspot.com is sicker than ever. How long will it take me to get this posted?