What prompted you to write your highly cited Physics Letters B paper?

Let me give you a bit of history. Basically, string theory has these ups and downs. Around 1993-1994 it was definitely a down. There was no hot topic, no focus; although some seeds of future breakthroughs were already in place. Before then I was working on these large N models a lot. I was trying this and that to generalize those models, and to bring out their connections with strings.

  What are large N theories?

In our world, we know that there are quarks and gluons and each quark comes in three different colors, and there is a symmetry that says you can essentially replace one color with another. This is built into the underlying gauge symmetry principle, which basically governs everything we're made of. So for large N theories, you imagine a generalization of our world where instead of quarks coming in three separate colors, each quark will come in "N" colors, where N is a very large number. A lot of people believe that an analytic approach to solving the more realistic gauge theories will come first through solving these large N approximations-something Gerard t'Hooft first proposed back in 1973-and then trying to work back to N equals three, which is our realistic case.

  Now back to the story of your Physics Letters B paper.

In 1995, there was a series of interesting developments, which led to this paper by Polchinski on D-branes, which are a kind of topological defect in space-a subsurface on which strings are allowed to end. This seems very simple, but it is a very important idea.

So after Polchinski's paper, I immediately started trying to do these calculations with D-branes, trying to understand how they interact with gravity-basically, studying the gravitational properties of D-branes. Then around that time, people realized that if you start stacking D-branes, you could make black holes. First, a seminal paper by Strominger and Vafa appeared, which studied a rather intricate arrangement of D-branes. Right around that time, I started studying D3-branes-three-dimensional D-branes. I found them more interesting because on these D3-branes, there live three-plus-one dimensional gauge theories; they are cousins of theories that describe the real world. With my student, Gubser, and another collaborator, Amanda Peet, we tried to do something like Strominger and Vafa did, but for D3-branes on top of each other. I think that was the smartest career move I ever made, but for some strange reason people didn't care about it for a couple of years. So I had quite a bit of time to look in detail at it, and I wrote several nice papers with several collaborators, and some of these papers stated essentially the same ideas of what people now call anti-de Sitter/conformal field theory (AdS/CFT) correspondence.

  And what is an anti-de Sitter space?

It's a space which is negatively curved, the antithesis to a sphere. A sphere is a positively curved space, which is completely symmetric. In other words, no point on the surface of a sphere is preferred to any other point. Anti-de Sitter space, or AdS space, is a negatively curved space, where again the curvature is the same everywhere. It is one of these classic spaces that people have been studying for many, many years, one of the simplest curved spaces in the books.

The point is that in the fall of 1997, Juan Maldacena wrote a paper saying essentially that you should take the limit where the three branes are replaced by this anti-de Sitter space. I just said that looks very interesting so let me try to translate what we've been doing with D3 branes into his language. Let me indeed take this limit, where you don't use the full three-brane but just use the anti-de Sitter space. So Gubser, my student at the time, and I started talking with Polyakov, who is another professor at Princeton who previously formulated similar relations between gauge fields and strings. We decided that we must formulate a way to calculate what are known as correlation functions. In gauge theory, you insert some operator at point one, another at point two, point three, and so on, and then you perform quantum averages over all fields and you want to know the answer. Our question was, what precisely is the answer? I said, "I already know part of it," but not everything. We tried to translate what we knew and what Maldacena said into one coherent picture and that's how we wrote that paper. So basically the formulation of this anti-de Sitter space/conformal field theory correspondence in its most crystallized form is attributed to three papers: the one by Maldacena, the one by us, and another one by Witten.

  What was the significance of the paper? Why was it so highly cited?

It gave a precise prescription of how it is that a string theory in anti-de Sitter space is dual to gauge theory. Maldacena said they must be dual but he didn't say precisely what it means; what is dual to what. And we answered those questions. Maldacena's paper appeared in November, and many people were reading it but they couldn't understand what the crux of the matter was. Then we wrote our paper in February, and put the paper up on the Internet with other concrete statements. At the time Witten was also thinking along the same lines. So in a matter of four days, he finished his paper and submitted it after ours. As you know, he's a very influential figure in the field, and it was nice for us that he basically stated the same prescription we stated.

So here were these two competing papers making a very beautiful statement of the relationship between string theory and gauge theory, a relationship many people had been looking for years. And it led to something truly outstanding: people just dropped everything and started working on this. Papers started appearing. It was immediately obvious to people in the field that they could do a whole bunch of calculations using ours and Witten's concrete prescription. And the amazing part is that it continues to this day.

  And where is all this work taking string theory?

Okay, what pure anti-de Sitter space describes is the duality of a so-called conformal field theory. It is a gauge theory that is the same at all energies; there is no preferred energy. That is certainly not our world. Our world is a gauge theory with a preferred energy scale. So people have been trying to push the correspondence to describe non-conformal gauge theories, like quantum chromodynamics (QCD), the theory of the strong force. That has been the focus of much of the effort, to bring this correspondence closer to the real world. I have been doing a lot of work on that.

  Is it making legitimate progress toward a true Theory of Everything?

What I'm talking about so far is going in another direction. It's going from a Theory of Everything toward the standard model. Once we started to say we found how gauge theories fit inside string theory, then we could ask why don't we just use string theory as a tool to solve some part or our low energy world that we know exists. QCD is a theory that has been formulated but that no one knows how to solve. So one possibility is to go from this super-duper mathematical structure of strings to help us understand our own low-energy field of QCD. Then there are various other goals; indeed, maybe we can use this new understanding to do what string theory has always been good for, namely trying to understand quantum gravity to build one new Theory of Everything. It is a somewhat different approach to the Theory of Everything than before. At least, it might give us a new twist on how to build a Theory of Everything.

  What is the biggest obstacle in the way?

Basically string theory is just darn hard. We know a lot about its various limits, but we would know a lot more, even about these gauge theory correspondences, if we could solve string theory better. We are probably just scratching the surface of string theory. It's a very very difficult subject. We're sure it contains many wonderful things, but we cannot solve it in most cases. 

There is, of course, another obstacle. In terms of trying to extrapolate string theory to really high-energy scales, the big obstacle is that we don't have any experimental hints. If we're going to start talking about new physics, which happens at energies, say, beyond a trillion electron volts, it would be great to have some constraints from experiments. Is there really low-energy supersymmetry? Until we know, it's going to be very difficult.

  How did you decide where to submit or publish your paper? Why Physics Letters B?

These days we don't worry too much precisely which journal to send a paper. The important thing is to post it on hep-th. The paper was short, letter-sized, but not so short we could send it to Physical Review Letters, because they have a very strict standard. So I said, "Oh, I'll send it to Physics Letters B."

  Did you expect it to be this highly cited?

I didn't have an inkling it would have this many citations, but I was in a hurry to get it out, because I thought we had something important to say and we were kind of nervous to finish it fast.

  If you were going to relive that period again, is there anything you would do differently?

My big regret is that there was this window of a few months where I probably could have said much more completely what the statement of duality was-this AdS/CFT correspondence. I was very close to making a very complete statement, but I missed my chance and Maldacena made a more complete statement on the duality first.

  Are you satisfied with how fast the research is moving?

Right now? Right now, I think it's slowed down a bit. I was pretty happy with what I'd done, say, between 1998 and 2000. I feel I was at home with this field and I capitalized on the insight that I built up from 1995. This last year I'm starting to feel more restless. I feel we have learned a lot, but there are hard problems we still don't understand, and I don't see the methods to break through these hard problems. Some kind of bypass is needed, and I don't know what it is. Now, again with Gubser and Polyakov, I am looking for possible bypasses.

  Is string theory going to be solved in our lifetime?

I'm not sure. In physics, some things never get completely solved. It's always a patchwork of partial understandings. I'm hopeful that we will learn a lot more than we know now. But we absolutely need experimental input to gain confidence in string theory as a Theory of Everything. On the other hand, I don't think it's going to go away. In our field, some things just disappear. They come up and get a lot of attention and then people lose interest. I'm fairly confident that this is not one of those things.  

Dr. Igor Klebanov
Princeton University
Department of Physics
Princeton, NJ, USA