# nLab Duff interview at M-Theory-Mathematics 2020

Contents

on the early history of and the perspective of M-theory.

# Contents

## Transcript

Q: You had codiscovered, early in the 1980s, some core ingredients of M-theory, like membranes. Later on, in 1995, this came to be known as “M-theory”. How do you reflect on that?

Duff:

(00:43) Reflecting on M-theory is quite a big challenge.

(00:49) The story of M-theory began with the story of eleven dimensions.

(00:54) It was 1978, I think, when Werner Nahm pointed out $[$Nahm 78$]$ that supersymmetry places an upper limit on the dimension of spacetime, which is 11.

(01:05) And so in the early 80s, my colleagues and I looked to 11-dimensional supergravity as a candidate for a unified theory of the fundamental forces.

(01:16) That involves compactifying the 11 dimensions down to 4.

(01:23) That had its problems. The theories we looked at were not phenomenologically very promising.

(01:31) Whether you have extra dimensions or supersymmetry, the problem still remains that Einstein’s gravity is incompatible with quantum mechanics, in the sense that the theory is not renormalizable in the sense of conventional quantum field theory.

(01:51) When string theory came along, in the 1984 string revolution, 11 dimensions got pushed to the sidelines, and we were told that 11 dimensions was barking up the wrong tree.

(02:08) But some of us thought, even then, that there is something not quite right: Why do superstrings live in 10 spacetime dimensions, if supersymmetry allows 11?

(02:24) The next major contribution was when Bergshoeff, Sezgin and Townsend discovered $[$Bergshoeff-Sezgin-Townsend 87$]$ the 11-dimensional supermembrane.

(02:35) For me that was the starting point of what I would call M-theory.

(02:42) Because it said: Fine, strings are fundamental and live in 10 dimensions, but you have these membranes, which seem equally fundamental, living in 11 dimensions.

(02:55) My colleagues and I – Stelle, Howe, Inami – were able to show $[$Duff-Howe-Inami-Stelle 87$]$ that if you wrap this 11-dimensional membrane around a circle, it looks like a 10-dimensional string, in fact it looks like the type IIA string.

(03:14) So for us, that is proof, if proof is needed, that membranes in 11-dimensions were part of the big picture, including strings.

(03:26) However, that view was not a popular one, I have to say.

(03:31) The overriding view at that time was that spacetime had 10 dimensions, it was occupied by strings, which were the theory of everything, and all these other objects, these branes, were theories of nothing.

(03:46) That was the conventional view.

(03:50) So in the early 90s, there were sort of two communities, if you like: The string people were doing their thing in 10 dimensions; the membrane people were doing theirs in 11; and it wasn’t clear if we were on the same page, or what.

(04:06) And then, as you know, Edward Witten made this startling speech at the University of Southern California $[$Witten 95$]$, where he pointed out that the five consistent string theories and 11-dimensional supergravity were not, as we previously thought, six rival Theories of Everything: They were six different corners in the deeper and more profound theory that he called “M-theory”.

(04:38) Now, given that we have been arguing in favour of membranes, the fact that the theory got called “M” was something of a Pyrrhic victory.

(04:50) It was saying: “Well, maybe membranes, we’re not completely sure.” $[$see Hořava-Witten 95, p. 2$]$

(04:56) For me, anyway, it was clear that branes were just as important as strings.

(05:05) Joseph Conlon, writing in a recent book on string theory, says that when he saw our paper $[$Duff-Howe-Inami-Stelle 87$]$ about wrapping the brane around the 11th dimension, from the late 80s, he was shocked, because the history of the theory that he had been brought up with would not allow such a thing until 1995.

(05:31) So, M-theory had a strange history.

(05:38) I could summarize my research in the early 1980s as arguing for spacetime dimensions greater than 4, and for worldvolume dimensions greater than two in the late 80s, and that struggle was by far the harder of the two.

Q: Similarly in the late 80s, also the regularized quantization of the super-membrane led to the matrix model, which later on was re-discovered as D0-brane quantum mechanics, and then hailed as a contender for a definition of M-theory. How do you reflect on this curious M-theory conceivement?

Duff:

(06:30) It was quite usual for discoveries that were made in the 80s to re-appear in the 90s.

(06:39) I don’t want to diminish the importance of the matrix model. It was very important. They built on earlier work – for what we would now call D0-branes – of the late 80s.

(06:59) But the matrix model itself was not all of M-theory; it was a corner of M-theory, and it told us certain interesting things, but there were interesting things about M-theory that it didn’t tell us.

(07:13) I think we are still looking, in fact, for what M-theory really is.

(07:19) We have a patchwork picture. We understand various corners. But the overarching big picture of M-theory is still waiting to be discovered, in my view.

Q: In your famous review “M-Theory (The theory formerly known as strings)” $[$Duff 96$]$, in the concluding section, you wrote: “The overriding problem in super-unification, in the coming years, will be to take the Mystery out of M-theory, while keeping the Magic and the Membranes.” What do you think is the status of this “overriding problem” today?

Duff:

(08:08) It’s still there, of course.

(08:12) M-theory in 1995 was very promising, and it’s taught us a lot about the fundamental interactions; but the final theory is still not with us.

(08:24) My view, and I consistently held this view since I first started in quantum gravity is that we have to take a long-term stance.

(08:37) There’ll be no overnight miracles; we have to keep beavering away, chipping away, and hopefully, one day, we’ll find the answers.

(08:48) I am optimistic that there is an M-theory without nagging mystery, but I wouldn’t like to put a time-scale on how long it’s going totake us to find it.

(09:01) My argument would be for patience.; this is what we need right now. Of course that’s not popular with the journalists, or for quick gratification.

(09:16) But if we look at the discussions that had the greatest impacts, recently: the Higgs boson took 50 years between its prediction and its discovery; the cosmological constant, if indeed that’s what dark energy is, would be a hundred years between the prediction and the discovery; similarly gravitational waves.

(09:42) There is no reason to think that a Theory of Everything is going to come along any quicker than these other discoveries.

(09:51) We just have to keep hoping for the best.

Q: In the late 90s you wrote in Scientific American $[$Duff 98$]$ and also in your book on M-theory $[$Duff 99$]$: “Future historians may judge the late 20th century as a time when theorists were like children playing on the sea shore, diverting themselves with the smoother pebbles or prettier shells of superstrings, while the great ocean of M-theory lay undiscovered before them.” How do you look at his prediction 20 years into the 21st century?

Duff:

(10:30) I hope you recognize that most of these words were of Isaac Newton, I just made a few substitutions in the right places.

(10:40) I still hold the view that perturbative 10-dimensional strings, as they were pursued in the late 80s, will be seen to be a small corner of the final theory.

(10:57) That’s not a view that’s necessarily shared by others: Ed Witten, in fact, wrote to me, after I wrote that, to argue that he didn’t share that view.

(11:10) There is a certain faction that believed that strings are more fundamental than branes, because string theory admits a perturbation expansion.

(11:23) But in my view, that’s not the criterion for what is fundamental and what isn’t.

(11:29) God does not do perturbation theory, perturbation theory is what we do because we don’t know any better.

(11:38) So the fact that branes do not admit a perturbative treatment, as strings do, is not, in my view, a reason for thinking that branes are less fundamental than strings – especially since strings are just a limiting case, as we see, of branes.

(11:58) I don’t see how you can maintain that one object which is not fundamental has a limiting case which is.

(12:08) So we have to treat them democratically.

Q: In your interview by Farmelo, last year $[$Farmelo interview Duff$]$, you said: “The problem we face is that we have a patchwork understanding of M-theory, like a quilt: We understand this corner and that corner, but what’s lacking is the overarching big picture. So directly or indirectly, my research hopes to explain what M-theory really is. We don’t know what it is.” Do you have a hunch what form the answer might eventually take?

Duff:

(12:44) No, actually I don’t know.

(12:46) I wouldn’t like to predict what the ultimate picture of M-theory will be; I imagine it will be something quite different from what we can imagine now.

(12:58) Going back to how the M-theory has developed:

(13:05) One curious feature of the big story is the AdS/CFT correspondence. Because when Maldacena wrote his paper $[$Maldacena 97$]$, he had three examples: $AdS_4 \times S^7$, $AdS_5 \times S^5$, $AdS_7 \times S^4$. Two of those were 11-dimensional M-theory, compactified, and the other one was Type IIB.

(13:34) But if you look at the papers that have been written since Maldacena’s seminal contribution, the vast majority of them have been on the $AdS_5 \times S^5$-story.

(13:48) There hasn’t, for whatever reason, been the same progress in M-theory, as a result of that.

(13:58) The AdS/CFT correspondence in a way diverted attention away from the goal of finding a unified theory of all the fundamental forces, starting from 11 dimensions.

(14:13) It’s been tremendously successful in its own right, Maldacena’s paper $[$Maldacena 97$]$ is the most highly cited paper in history.

(14:22) But it has not, strangely enough, contributed to how we unify the strong, weak and electromagnetic forces with gravity. At least I don’t think it has.

(14:35) That’s a different problem.

(14:38) I would have been happier, I think, looking back, if we were further down that road, since 1995, than we are.

(14:48) But I am still optimistic that we are on the right track.

Q: So you believe we ought to get back to the original big question about: what’s the nature of M-theory.

Duff:

(15:03) That’s my view, yes.

(15:05) But of course, in order to do that, you have to have some good ideas. We need more good ideas.

Q: In that same interview with Farmelo, you said: “In a certain sense, and this is not a popular statement, I think it’s premature to be asking: ‘What are the empirical consequences?’, because it’s not yet in a mature enough state, where we can sensibly make falsifiable predictions.” Would you like to expand on that?

Duff:

(15:39) Yes, it was harking back to the remarks I made a few minutes ago, about the timeline between the germ of a theoretical idea and its ultimate empirical confirmation.

(15:53) Another good example would be quantum entanglement: The problem was spotted in the 1930s, by Einstein, Rosen and Podolsky, but it wasn’t until the 1960s that John Bell came up with a falsifiable prediction, and it was another 20 years before Alain Aspect did the experiment.

(16:19) My view is that Theories of Everything are going to similarly require a large timeline between the original idea and the confirmation.

(16:36) That’s why I think M-theory is not yet in a mature enough stage for us to make falsifiable predictions.

(16:44) We don’t understand the theory sufficiently well yet to do so.

Q: Should we try to focus on understanding it first, and then it would naturally give us predictions?

Duff:

(17:00) That’s what I would recommend.

(17:03) But of course progress comes in directions that you often don’t expect.

(17:11) So I don’t want to predict that progress will come from a particular direction.

Q: A similar point was made recently by Tom Banks, in a critique of the 15 year old discussion of the landscape of de Sitter vacua $[$Banks 19$]$. Do you think it’s possible that an actual formulation of M-theory will show of the putative landscape of string theory is not actually there?

Duff:

(17:59) Superficially, I would say No, because M-theory has even more vacua than string theory has.

(18:07) The landscape problem is not going away.

(18:13) What’s often not appreciated, though, is that if you follow the critics in string theory and M-theory and stop doing them today, and start tomorrow with a blank sheet of paper and a sharp pencil, and say: “Where do we go from here?”, the landscape problem would still be there!

(18:36) The problem of why you pick one physical vacuum from an infinity of mathematically possible vacua is a problem that is going to be there whether you do string theory/M-theory or not.

(18:55) I am agnostic about the multiverse. I don’t know whether we live in one universe or many. But there, again, we have to keep beavering away, and hopefully the truth will out.

Q: Do you envision any role for mathematics? If you are able to map M-theory to mathematics, would you think mathematics would have something to say?

Duff:

(19:25) It certainly does, because in the absence of empirical data, what do we have to guide us? We have consistency as our criterion.

(19:37) Whatever our theories are, they must be, first of all, mathematically consistent – no self-contradictions – and they must be consistent with what we already know to be true.

(19:51) This is, in a way, a straightjacket, that constrains our speculations and our projections where the theory is going to go.

(20:03) And its a very severe straightjacket: We can’t just dream up any old thing and expect it to be mathematically consistent, or consistent with our knowledge.

(20:17) Mathematical consistency has a vital part to play.

(20:21) As you and your colleagues are aware, sophisticated mathematics is becoming more and more important in understanding M-theory; and it is going to require the kind of mathematical approaches that you are doing.

(20:37) You’ll sort it all out, I am sure.

Q: How do you envision the future of activity in M-theory should look like?

Duff:

(20:54) There again I don’t want to make any rash predictions.

(21:00) My view of research is a Darwinian one: You find the brightest people, you give them the money, you let them get on with it and they will go wherever they will go. I don’t think one should try and engineer, from above, the directions that research should take. Let the imagination of the best people – let their imagination run them, and we’ll see where it takes us.

A commented collection of the early articles on the super-membrane and what came to be called M-theory:

Further early exposition of M-theory:

category: reference

Last revised on January 26, 2023 at 12:25:38. See the history of this page for a list of all contributions to it.