Brane - Interview with Dr. Michael Duff

pecial Topics correspondent Gary Taubes recently spoke with Dr. Michael Duff of the University of Michigan about his highly cited work in brane theory. Our Special Topics analysis of work in brane theory over the past decade ranks Dr. Duff at #5 among scientists by total citations, with 40 papers cited a total of 1,707 times. Dr. Duff’s most-cited paper is "String solitons," (Phys. Rep.—Rev. Sect. Phys. Lett. 259 [4-5]: 213-326, August 1995), which has been cited just over 300 times to date, ranking at #12 among brane theory papers of the past decade. Dr. Duff’s work is also well represented in the ISI Essential Science Indicators Web product, with 55 papers cited 2,257 times in the field of Physics since 1991. Dr. Duff is the Oskar Klein Professor of Physics and Director of the Michigan Center for Theoretical Physics at the University of Michigan in Ann Arbor.

Let's begin at the beginning: What exactly is a soliton?

You can think of it as an object that has finite energy and particle-like behavior. It's a particle that is not in the equations of string theory in the beginning, but then emerges as a solution to the string equations. The classic example of this would be in four-dimensional gauge theories, like the kind of theories that describe our universe. You start with electrically charged particles like quarks and W bosons, but you then discover that the theory permits magnetically charged soliton solutions, known as monopoles. So the full particle spectrum includes not just the electrically charged particles you first considered, but also magnetically charged soliton particles. Then there are branes, which are higher dimensional analogs of the monopoles. You start with equations that just describe a string-like object, but you discover the string equations have as their solution other extended objects that are the branes. Therefore we call them soliton branes.

I first got interested in branes because I'd been working on another theory—11-dimensional supergravity—even before the first string revolution in 1984. What was interesting is that 11 dimensions is the maximum dimensions that supersymmetry allows. But string theory was a 10-dimensional theory with supersymmetry, and it was always a mystery to me why a Theory of Everything should be 10-dimensional when supersymmetry allows for 11 dimensions. When the idea of a super-membrane—a brane—came along in 1987, it lived in 11 space-time dimensions. At first it seemed that you had two rival activities: the 10-dimension string theorists and the 11-dimension membrane theorists. It wasn't clear they were on the same page, or whether they were pursuing different goals entirely. Around 1990, it was realized that some branes were solutions of the string equations of ordinary 10-dimensional superstrings. And that’s where the soliton idea comes in. You discover that these equations for strings have as their solution these extended objects called solitons.

Why do you think your string soliton paper had such impact?

First of all, this was a Physics Report, which means it was in the nature of a review article, although there was some original material in it. Basically, we had collected the work that the three of us had been doing over the previous four years on soliton solutions in string theory. The other reason it was so highly cited was that, although we didn’t know it when we wrote the paper, it subsequently became part of the M theory revolution.

Okay, what is the M theory revolution and why did that give your paper such impact?

In 1995, we had all these ideas floating around—11-dimensional supergravity, 10-dimensional strings, branes—and they suddenly crystallized into what we now call M theory. And that's what you might call the second string revolution or the M theory revolution of 1995. We wrote our paper at the end of 1994, at a time when there was some interest in branes and some in string solitons, but it was still not what you might call mainstream. Then in 1995, it was realized that M theory not only incorporates all the old ideas of 10-dimensional strings but it also incorporates the older ideas of 11-dimensional supergravity, which I'd been working on for a long time, and it incorporates all the brane ideas, too.

Is M theory one theory?

It is one unique, all-embracing M theory.

And what does "M" stand for?

According to Dr. Edward Witten, who coined the phrase, "M" stands for "magic," "mystery" or "membrane," depending on your taste. The reason for this sort of humorous absurdity is that although M theory describes all of string theory and all the branes and so on, we still only have glimpses of what the full theory actually is. We understand various corners of M theory, but we don’t have any over-arching picture of what this ultimate unified theory actually is.

So how exactly did M Theory bring string solitons into the mainstream?

Before 1995, string theory was facing certain big questions. One was the uniqueness problem: we had five consistent string theories, each of them mathematically unifying gravity with the other forces, but they seemed to be different theories. Five Theories of Everything was an embarrassment of riches. The first thing M theory did was to unify all those diverse ideas. The five string theories now can be seen as just five different corners of this deeper M theory.

The second thing M theory did is a little more technical and requires some explanation. We can't solve the equations of string theory exactly. In that respect, it's like all other theories we've written down. We have to resort to some approximation scheme, and the time-honored scheme is called perturbation theory. It means you pick some small number in your theory and you do what's called an expansion in powers of that small number. That only takes you so far; however, there may be all kinds of questions you would want to ask that are beyond the reach of perturbation theory. What M theory did is give you a window on what we call the non-perturbative regime, where these small numbers I'm talking about are coupling constants that tell you how strongly strings interact with each other. Until then, we didn’t have a way of understanding strongly interacting strings in which the coupling constants are not small. M theory gave us a window on that, and we could now answer all kinds of non-perturbative questions that we couldn’t answer before. The solitons are part of this non-perturbative structure, because their mass depends inversely on the coupling constant so you would never have seen them in perturbative theory.

And what's the payoff as far as making progress in string theory?

The first payoff, as I mentioned, is unification. We now have one theory rather than five. We're happy about that. It also includes the 11-dimensional theory. So that resolves the mystery of why supersymmetry allows 11 dimensions not 10. What does it do for you? One thing it does, to pick some specific examples, is to explain some things about black holes. In the mid 1970s, Hawking told us that black holes weren't as black as they were painted. Rather, they radiate energy. So they have this temperature, and what we call an entropy, associated with them. Hawking wrote down the formula for what that entropy should be. It's a famous formula that says the entropy is one-quarter the area of the event horizon of the black hole. He used a kind of macroscopic thermodynamic argument to reach this conclusion, but if what he was saying is correct, there should also be some microscopic explanation. In the subsequent 20 years, nobody could figure out what this microscopic origin of black hole entropy actually was. Using these new ideas of branes and M theory, that problem has now been solved. Another thing it does, and this may be too early to tell whether it's good or not, is M theory now offers dozens of ways of trying to do a real-world analysis to see how the standard model of particle theory fits into the scheme of things. Depending on how you look at it, that can be good or bad. Now we're left with a different kind of uniqueness problem. How does nature single out the one way of doing things? It also means we have some new avenues of exploration that we didn't think were open to us before. And then there's this large-dimension industry, which is a spin-off from M theory, as well.

Are you satisfied with the present pace of progress in your research?

Well, you can't have revolutions continually. They happen, and then you have periods of consolidation—less exciting, perhaps, but necessary periods—in which you calmly evaluate where you are and where you're going. I think that’s the phase were in now, after a spurt of activity that started in 1995 and went on for a couple of years. Now we're back in that where-do-we-go-next phase. Obviously, I would prefer if I knew the answer to that, but I can’t really complain. We've learned an awful lot in the last five years that we had never dreamed of before.

What is the greatest challenge at the moment?

I think there are two. One on the theoretical side, and one more on the reality side. The theoretical one is to pin down exactly what M theory is. We know that in the limit of low energies it is approximated by 11-dimensional supergravity, a theory we've studied for many years. We know that when the coupling constant is weak, it is approximated by one of the five consistent superstring theories, depending on how you take your limits. We know that lots of these different theories are related by what we call dualities. So we know lots of properties of M theory, but we can't actually put a finger on what it is. That’s the theoretical challenge: to rigorously pin down what this all-embracing theory really is.

The other challenge is to make contact with experiment. How do we explain the standard model of particle physics? How do we explain Big Bang cosmology and other things, starting from this 11-dimensional M theory? I don’t honestly know how soon, if ever, that problem will be solved. We're facing again the uniqueness problem: this 11-dimensional theory has lots of different solutions. Some involve dimensions being curled up; some don't. Even for those that curl up the right number of dimensions—seven—there are still billions of different ways of doing it and each gives a different four-dimensional model of elementary particles. Some look vaguely realistic. Others look nothing like the real world. What we're lacking is a guiding principle to tell us how to pick the right solution out of this zoo of different solutions.

So those are the things I would identify as the two big problems: What is the theory? How do we make realistic predictions? They're fairly big problems.

Are you optimistic?

Yes, I'm optimistic, but what I wouldn’t like to get into is the time scale involved. Let's take the Higgs boson, for example. It was predicted in 1964. Even if they discover it on target in the next round of accelerators, you still have a 40-year gap between the theoretical idea and the confirmation. The same is true of gauge theories. Yang and Mills wrote down the equations in the mid-1950s, but we didn’t discover the W boson until the early 1980s. The same goes for supersymmetry. If we discover that, it will still be at least 35 years since we first wrote down the theoretical ideas. And M theory is much more ambitious than any of those are. It's a Theory of Everything. I don’t expect the time scales to be any shorter. It could be decades more before we confront theory with experiment and can tell whether it's the right theory or not. On the other hand, it could happen next week. Who knows? I'm not looking for instant gratification, however. I'm looking to be a little bit patient.

Dr. Michael Duff
University of Michigan
Department of Physics
Ann Arbor, Michigan, USA

ESI Special Topics, April 2002
Citing URL - http://www.esi-topics.com/brane/interviews/MichaelDuff.html