Matrix string theory
Hi physics fans,
I was told that someone wrote that I wrote that I discovered Matrix theory. Well, it is not the case. A similar statement that would mostly be correct would have to talk about "Matrix string theory", not "Matrix theory".
These are two different things.
"Matrix theory" was the first known way to define M-theory in 11 dimensions using a quantum mechanical model that involves a couple of matrices - the quantum-mechanical operators x,p (transforming as nine-vectors) have two extra indices m,n that go from 1 to N - therefore the operators x,p behave as matrices. Well, there are also some fermionic matrices that transform as spinors.
The Hamiltonian of this Matrix theory is the dimensional reduction of the 9+1-dimensional supersymmetric Yang-Mills theory down to 0+1 dimensions (0+1 dimensions means that the time - the number 1 - is the only continuous variable on which the operators depend; therefore we deal with a quantum mechanical model, not a higher-dimensional field theory).
The authors of that paper (Banks, Fischler, Shenker, Susskind i.e. BFSS)
http://arXiv.org/abs/hep-th/9610043
have explained that this simple matrix model in fact contained the whole physics of 11-dimensional supergravity including the membranes (this was mostly known before BFSS - a paper by de Wit, Hoppe, and Nicolai) as well as the correct high-energy completion of this theory - that is called M-theory. Matrix theory provided us with the first known definition of the 11-dimensional magical M-theory; the word "Matrix" became another justification of the letter "M" beyond Membrane, Mother, Magic, Mystery (or upside-down "W" for "Witten", as Glashow said).
Matrix string theory was started by my paper (L.Motl)
http://arXiv.org/abs/hep-th/9701025
Well, originally the matrix strings were called "screwing strings" and I had no idea about the extra meaning of that phrase. A more complete work on the same subject was - sort of independently - written 2 months later by more renowned scientists, namely Dijkgraaf, Verlinde, Verlinde (DVV).
http://arXiv.org/abs/hep-th/9703030
They were able to use conformal perturbation theory to describe the details of the interaction process. See our recent paper with Dijkgraaf
http://arXiv.org/abs/hep-th/0309238
to see some new progress in the field, as well as the fact that we talk to one another :-) although, of course, I must confess that I find it a bit annoying if I see a paper that talks about matrix string theory and cites DVV only. But this is not DVV's fault, I would say. ;-)
Another early paper on Matrix string theory was written (before DVV) by Banks and Seiberg (an extension to type IIB string theory and so on),
http://arXiv.org/abs/hep-th/9702187
Matrix string theory (MST) is, unlike the original BFSS Matrix theory, a 1+1-dimensional super Yang-Mills theory on a cylinder: the spatial dimension is compactified. An essential feature of this theory is that there are long/matrix/DVV strings that can be wound around the cylinder. MST was the first known nonperturbative definition of string theory - something that string theorists had dreamed about for years - that could have been showed to reduce to the well-known perturbative calculations in the limit where the coupling constant is small, and it convinced many that the Matrix theory is correct, indeed.
I apologize for the graphical imperfections of this text; it is my first posting here.
All the best,
Lubos
. For sure a lot of people will have questions for you!
