[Warning! This is an unusually technical post.]
So it is an interesting fact that in 1992, after my phd advisor Tim Morris wrote his last paper with me, he never wrote a string theory paper again….until last week. (No, I don’t think it was because of the horror of working with me…. so stop thinking that right now!)
I always considered it a great loss to the field, over the years, as he is quite a remarkable fellow (hey – he seems to have been lauded at a national piano competition again!), and several things happened in the field after he left that I always thought that he would enjoy, and moreover bring an interesting and valuable approach to. On the other hand, he was not lost to physics or high energy physics as a whole, and started a series of really creative and singular work in another area, as I’ll mention below. (Ironically, the scope of some of what we did in that last paper we wrote, with Simon Dalley and Anders Watterstam, has only been fully appreciated in some recent work of mine (with Durham Phd. student James Carlisle and USC undergraduate student Jeff Pennington), described in an earlier post. We knew in 1991-2 that we had something that would now be called “open-closed duality”, but it is part of an even nicer story, as partially uncovered by Klebanov, Maldacena and Seiberg….. read that post for more, and I should do the next part of that story one day.)
So whenever I ran into Tim over the years (sadly, only a very few times since I left) I would rekindle that hope that maybe he’d return to the fold again. I actually had already decided (in my mind) that the best place for him to re-enter the field again might be via what he went off to do. You see, he’s been developing a remarkable scheme for computing in gauge theory, based on the Wilsonian description of RG flow. The scheme allows you to compute using methods completely different from the usual (Feynman diagrammatic). One of the problems that Tim solved was how to make this scheme work for gauge theories. How to do the “Exact Renormalisation Group” (ERG) as it is called scheme in a manifestly gauge invariant way? The whole concept of a cutoff in a gauge theory is plagued by difficulties of definition, at least in the usual approaches we teach our graduate students. Well, it turned out that it is possible, but it required the embedding of the SU(N) gauge group into a supergroup, SU(N|N). (See here and here.) Hmmmm? you might ask… but it works. Well, I kept thinking that surely, this had to make contact with this other way we know from string theory of doing manifestly (non-Feynmann diagrammtic) computations in SU(N) gauge theory, the AdS/CFT correspondence. Further, we know that radial direction in the AdS part of the spacetime is some sort of gauge invariant definition of a cutoff. Clearly, there is “some money to be made” (ho ho ho) in connecting these two approaches. They cannot be unconnected, at least in my mind.
Well, the good news is that last week, Tim returned to the fold, and this is precisely the way he chose to take back home to the world of string theory with a new paper (with Evans and Rosten) showing the connection explicitly. (Welcome back Tim!) I believe that my former fellow Southampton graudate student, my sometime collaborator, and faculty colleague of Tim’s, Nick Evans, had a lot to do with his return (well done Nick!) since in the past he and I have sat and speculated about the content of the above paragraph’s expected connections, and whether we could interest Tim in it or not. I never really understood enough of the ERG approach to know how to proceed, but I did promise myself to look out for a natural appearance of SU(N|N) gauge groups in the context of strings. That was to be my hook….
Well, I missed it. Just been too busy. The paper that had SU(N|N) came out and I missed it, and frankly I feel a bit of a plonker. A few weeks ago, Okuda and Takayanagi wrote a paper introducing the idea of “Ghost D-Branes” (see here) which shows you very naturally how to make SU(N|N) gauge groups. As soon as you see that, and what the role of the ghost D-branes is, it is clear how to AdS/CFT-ize it and make quite natural contact with what the ERG scheme achieves….. This is what Nick Evans, Tim Morris and Tim’s student Oliver Rosten (who gave us here at USC an excellent seminar on the ERG scheme last year, by the way) did in their paper, which is cute, straightforward and all of six pages. Have a read of it. There’s a lot more to be done there, I’m sure.