## Nima Arkani-Hamed on Maximally Supersymmetric Theories

#### Special Topic of Supersymmetry Interview, June 2012

Arkani-Hamed’s work also appears in Since 2008, he has been a professor at the Institute for Advance Study in Princeton, NJ. |

Below, Arkani-Hamed discusses his supersymmetry theories with ScienceWatch.com correspondent Gary Taubes.

**You’ve worked on a lot of different aspects of theoretical physics over the years. How much of that has been on supersymmetry? Do you consider yourself a **

**supersymmetry researcher?**

Even classifying researchers as “supersymmetry people” or not is a little funny. Supersymmetry is such a deep and fundamental idea that everyone in the field is a supersymmetry person or uses supersymmetry in some crucial way at some point in their research. It’s really one of the ideas that permeate all of fundamental theoretical physics. So the question of whether you’re working on it or not is really more a question of whether the word is in the titles of your papers or not, but it’s there all the time.

More specifically, when I was a graduate student, I worked a lot on the phenomenology of supersymmetry—how it might show up in accelerators and solve various particle-physics problems. I worked on other things as well. Over the past 10 years, I have come back again and again to thinking about assorted variations on and different aspects of supersymmetry. In just the past two or three years, I’ve gotten involved in a quite different line of investigations which is much more heavily dominated by supersymmetry. The motivation is to understand scattering properties of good old-fashioned gluons, the kind of thing Feynman told us how to solve 50 years ago.

It turns out there’s a really extraordinary structure that seems to underlie these seemingly mundane particles, and that’s a whole other story. But it also turns out that the simplest possible place to understand these things is not just in theories with a little supersymmetry but in theories with as much supersymmetry as we can possible have, known as “maximally supersymmetric” theories.

**Can you explain to us some of the places where supersymmetry shows up in these various theories, and what it does for you when it does show up? **

Let me back up for one second here: Supersymmetry is an extension of the symmetries of space-time, and it has this really interesting character. On the one hand, supersymmetric theories are examples of ordinary quantum field theories. They’re not radically outside the framework of the rubric handed down to us by our ancestors by the 1930s. But on the other hand, while being ordinary quantum field theories, they have extraordinary properties; they extend the symmetries of space-time. And so they fit at a nexus between two worlds. Considering this deep, central idea, it’s not surprising that it’s going to show up in a host of places.

One of the places it shows up is in attempts to extend, very pragmatically, the standard model of particle physics and to solve a variety of its problems. So there are these famous fine-tuning problems and other difficulties we have, which can be summarized as attempts to understand the following major puzzle: Because of quantum fluctuations—violent vacuum fluctuations that get more and more violent as you go to shorter and shorter distances—it seems to be impossible to have any macroscopic order in the universe at all. The universe is big, gravity is weak; there is a very big macroscopic universe, but that seems almost impossible given that there are these gigantic quantum fluctuations.

Supersymmetry is one attempt to solve these problems by coming up with an explanation for why the quantum fluctuations disappear at short distances. This isn’t a small problem, a details thing. If you’re going to fix it, it’s going to need a big fix. The way supersymmetry does it is by extending the idea of space-time, and it does it in a way that you can’t fluctuate at all in these quantum dimensions. There’s a perfect symmetry between the quantum dimensions and the ordinary dimensions, and so the gigantic quantum fluctuations have to cancel out. That’s why it showed up and people care about it a lot in particle physics and in finding extensions of the standard model.

It also shows up all over the place in string theory, because if you’re going to have a quantum mechanical theory of gravity, which is what string theory is about, one of the first things it should do is give you a nice big macroscopic universe to play with—even a toy universe. Any other attempt to talk about quantum gravity just fails at this starting point, because of exactly the same violent quantum fluctuation problem. So supersymmetry shows up because it allows us to get going and even talk about it. It also shows up for other reasons.

It turns out that just the structure of quantum field theories—how to calculate with them, and see what the consequences are—is very rich, very complicated, and difficult to calculate with. When the couplings between quarks and gluons get strong, it’s impossible to calculate anything analytically, and for a long time people had no idea how to make progress. Supersymmetric theories have so many theoretical properties that you can really make wonderfully significant progress studying the dynamics of quantum field theories. And you do it by studying them in their most supersymmetric aspect first.

Supersymmetry is such a deep and fundamental idea that everyone in the field is a supersymmetry person or uses supersymmetry in some crucial way at some point in their research. It's really one of the ideas that permeate all of fundamental theoretical physics.

**SW: A decade ago, physicists seemed obsessed with minimally supersymmetric theories. Now you’re talking about maximally supersymmetric theories being absolutely fundamental. What changed in the meantime, and what drove that change? **

One of the things we’ve realized recently is that the theory with the most supersymmetry, this maximally symmetric theory, seems to be like the harmonic oscillator of the 21st century. It looks like the simplest possible nontrivial quantum field theory in four dimensions, and so we just had to learn how to solve it. Just like people learning how to solve quantum mechanics; in the end they had to understand these simple theories inside out—the hydrogen atom and the harmonic oscillator. It looks like we have our hydrogen atom or our harmonic oscillator, but in the 21st century this is this maximally supersymmetric theory.

More formal people and string theorists have been interested in theories with a lot of supersymmetry for a long time, partially because the theory in 10 dimensions actually contains all this extra supersymmetry—and where the theory looks simplest is where it has all the extra supersymmetry. But string theorists were pretty obsessed with getting down to four dimensions and having realistic theories, and so maybe they didn’t spend as long as they should have studying these maximally supersymmetric theories. Part of the consequence, though, of the second string revolution, which culminated in this famous correspondence between theories of gravity and quantum field theories, was this focus on these maximally supersymmetric theories and how remarkable they are.

Now let’s descend from these lofty heights to something which seems like a much more mundane question. You want to discover new physics at an accelerator like the Large Hadron Collider (LHC), but in order to do so you have to subtract out what you think of as the mundane background from ordinary standard model interactions. Say you want to collide two protons, and the gluons inside those particles collide and produce an exciting superpartner. Well, those things very quickly decay to ordinary gluons again and maybe some other particles, but the kind of thing you’re looking for is two gluons go in and, say, four gluons go out. The rate at which this happens with ordinary processes—producing these superpartners—would be, if we’re lucky, maybe once a minute. But exactly the same final configuration is produced by ordinary standard-model particles hundreds of thousands of times a second.

So you really have to understand the rate at which that’s happening ordinarily and then subtract it to see something exciting. It sounds like a grungy, dirty job that someone has to do: Sit down, grind out all these dirty calculations, and actually predict what the rates are.

What people started discovering in the 1990s is that these calculations are really, really hard but that somehow there are magical simplifications in the maximally supersymmetric theory. They noticed that the answers were a lot simpler. Ironically, what they were doing is that, in order to calculate the ordinary standard model processes to discover the minimal supersymmetry, they were using the maximal supersymmetry in their calculations. Even just trying to do these mundane calculations, people found it was incredibly useful to cast the calculation first in the maximally supersymmetric theories.

At first that seemed like a bunch of tricks, but more and more, in the last five years, it’s become clear that there’s yet another formulation of good old-fashioned quantum field theories, which casts this picture—of the scattering of particles coming in and out—in a totally different light. It doesn’t involve a space-time picture. Totally different mathematical structures are starting to make an appearance. There’s something extraordinary going on. At the moment, again, this is all simplest and best understood in the context of these maximally supersymmetric theories.

There’s also really a sense of where this theory might be solved exactly. Just as a theoretical accomplishment, that would be a spectacular thing. It really might be possible that it will be solved in not too long.

**If you solve it exactly, what do you get? **

If we solve it exactly, we should be able to understand a huge number of things. That should shed some light on where space-time in quantum mechanics comes from. And secondly it should shed a lot of light on this correspondence between gauge theories and gravity. We should be able to understand how the two things map to each other. It looks like this is the next thing on the chopping block.

**To continue our descent to more mundane heights: Your most-cited paper of the past decade was a 2001 paper from Physics Letters B: “Electroweak symmetry breaking from dimensional deconstruction” (Arkani-Hamed N, et al., 513[1-2]: 232-40, 2001), now cited more than 600 times. What were you trying to accomplish in that paper, and why has it been so influential? **

Actually, that paper is only loosely related to supersymmetry. In it we manage to find a class of theories that addresses this problem of removing big quantum fluctuations in a more modest way than supersymmetry does. Okay, so there are these big quantum fluctuations that cancel when you add the contributions of the superpartners. It’s something you see vividly when you do explicit calculations: you have an ordinary contribution, you have the contribution from the superpartners, and because the superpartners have a different spin than the ordinary partners, there’s a precise cancellation. It’s very beautiful.

What we found was another class of theories that had another sort of symmetry—not a supersymmetry, but another sort in which the cancellation could be seen in a very similar way. But unlike supersymmetry, where cancellations took place between particles of different spins and statistics—in this case, between bosons and fermions—the cancellations took place between bosons and bosons. It was a surprising twist, because there were all sorts of folk theorems saying you could not make these cancellations happen without supersymmetry. And this was a counter-example. That’s what was theoretically interesting about this idea. It provided a new mechanism for understanding, in this case, the problem with the weakness of gravity, the hierarchy problem. It wasn’t as ambitious as supersymmetry was. It’s more of a foil to supersymmetry in many ways.

It also has another interesting feature, which a lot of people explored: This class of theories can look very similar to supersymmetry at accelerators. So it’s a really interesting challenge. This class of theories also has partners—if not for everything, at least for many things. So, should something new show up at accelerators, it makes it quite a bit harder to distinguish between these theories. That’s something else that got people excited and sparked a lot of work.

**The LHC is running at CERN and quickly getting to the point, it seems, that it has to make a few discoveries, or otherwise theorists will have to rethink some theories. Are you anxious about supersymmetry and what this means for the theoretical framework of physics beyond the standard model, if it happens that nothing shows up? **

As to this question of whether we’re really worried that the whole structure is in a lot of trouble, given that nothing has been seen so far, my take is that I am not any more worried about low energy supersymmetry now than I was before the LHC turned on. There was some cause for concern even before the LHC, some disquieting reasons to be somewhat worried. As for what’s happened so far at the LHC, the regions of parameter space in supersymmetric theories that have been ruled out by the LHC are not cause for more worry. In fact, it’s about where it was before we had this information from the LHC. From another point of view, if supersymmetry does indeed provide this natural understanding of the hierarchy problem, it could well put in a more indirect appearance in a number of low-energy processes we could have looked for. It was not even insane for it to show up at earlier colliders, and for a while the fact that we haven’t seen these indirect processes has been a cause for some unease about these ideas.

**But if nothing shows up in the next year, can you say that at least some supersymmetric theories are on life support if not gone for good? **

No. And for the same reason that I can only say the other problems were a cause for unease. If we just ask from the bottom up, without any theoretical prejudice put in, what kind of particles must we see, what supersymmetric particles absolutely have to be there for supersymmetry to provide a natural resolution to their hierarchy problem, it is a small fraction of all the superpartners. There are some absolutely crucial ones that have to be there—the superpartners of the top quark and of the gluon. Those are by far the most crucial ones. The rest could be somewhat heavier and not affect this problem at all. And that kind of spectrum is far from dead. In fact, the most natural-looking spectrum is perfectly alive and well right now even with the LHC data. It’s going to be probed pretty soon. That’s the point of building this machine. It is going to probe these things. But a perfectly natural, beautiful supersymmetric spectrum from this bottom-up point of view is perfectly consistent with LHC data so far.

The reason people aren’t, well, super-optimistic, is that while this is all you need from the purely bottom-up point of view, any kind of additional theoretical prejudice of what would make things nice as we go to shorter distances would require other particles to come along for the ride, and we should have expected to see those things earlier—even before the LHC—or to see their indirect effects earlier.

Certainly in a year, and certainly by two or three, even the purely bottom-up part can easily be ruled out by the LHC. At that point it’s not a matter of unease or “I think this or that”—just some objective facts. If we don’t see the superpartner of the top, if we don’t see the superpartner of the gluon, supersymmetry is not a perfectly natural solution to the hierarchy problem—full stop. And then we have to start talking about how fine-tuned it is, and discussions like that. There is a place beyond which there is no wriggle-room of any sort, but we’re not there yet.

**Your second-most-cited paper from the last decade is the 2002 article, “The littlest Higgs” (Arkani-Hamed N, et al., J. High Energy Phys., 7: No. 034, 2002), with more than 400 citations to date. What was the context of that paper, and why has it been so highly cited? **

Incidentally, those first two papers are very closely related to each other. “The littlest Higgs” is a nicer implementation of the idea put forth in that first paper. The third-most-cited paper is “Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC.” That one was a direct reaction to this unease about low-energy supersymmetry. It evokes a whole set of ideas about why this idea of naturalness may not be a good guide to what we should expect at the weak scale and yet it tries to preserve all the good successes of supersymmetry. That’s much more directly tied to trying to realize the essential great content of supersymmetry, while at least confronting head-on these uneasy feelings about why it hasn’t shown up already.

Getting back to the Higgs: Yes, seeing a light Higgs is absolutely crucial for any of these ideas to be realized. As you know, we’re right now in the total endgame for discovering the light standard model Higgs. That’s very, very exciting. The fate of the light standard model Higgs is sitting there on tape, so to speak, as we speak, and people are analyzing the data right now. We should have some news by the end of the year, certainly by the spring. That’s extremely exciting, and the light Higgs just must be there for these ideas.

**Which are “these” ideas? **

All of them. There is a sharp lesson that was taken away by some experiments in the late 1980s and early 90s, at CERN and at SLAC, that measured very precisely the properties of the Z boson, and almost all of us drew a basic lesson from these experiments: That whatever the physics that breaks electroweak symmetry is, it has to involve something that looks like a light Higgs. It’s remarkable that you can draw such a conclusion without seeing the Higgs directly, but if there isn’t something like a light Higgs—if there are no new states associated with the breaking of electroweak symmetry up to 500, 600, 700 GeV—then we would expect that there’d be corrections of the couplings to the Z boson to ordinary particles at roughly the percent level, and what’s been measured were corrections at more like a part-per-thousand level. So there are a number of things that would have been roughly 10 times bigger if we didn’t have something like a light Higgs. And so these were very strong, if indirect, indications that there is something like the light Higgs. Almost identical sorts of arguments led people to correctly predict where the top quark would end up being.

So this sort of argument has worked successfully before. I would be extremely surprised if that basic question was wrong. Then there would have to be some maliciousness on the part of nature to actually conspire to have large effects in these obstruse things like the couplings of Z’s to electrons and quarks to all cancel out to make it look a lot smaller than it actually is. I strongly believe there is something like a light Higgs. And certainly in little Higgs theories and supersymmetry, there is a light Higgs and we have to see it.

**Does that mean you expect to see a light Higgs with precisely the properties predicted by the standard model?**

No, and that’s why this particular period is so exciting. If we actually don’t see the standard model Higgs—a Higgs that’s produced as in the standard model and decays as in the standard model—if there are things beyond the standard model, which most of us hope and believe, then it could well affect both the production and the decay of the Higgs particle. So if we don’t see what looks like a normal Higgs, just in the next few months—if the window closes completely—then my reaction will *not* be that there is no Higgs at all. My reaction will be that we’ve actually got some evidence that there is something beyond the standard model and that the Higgs is being produced and decaying in a different way. So if we don’t see what looks like the standard model Higgs, that would tell us there is something beyond the standard model, and that would be very exciting.

**Is supersymmetry necessary for our understanding of the universe to be correct, or can it simply not exist, and instead there’s some other theory be waiting out there to solve all the outstanding problems?**

It depends what you mean by “necessary.” It seems a lot more necessary for certain kinds of questions than for others. For instance, no one has really managed to come up with a deep short-distance theory for quantum mechanics and gravity that doesn’t involve supersymmetry in some important way. And so that argues for some necessity, for supersymmetry, somewhere near the Planck mass at least.

Another deep thing about supersymmetry is what I previously mentioned: It makes the macroscopic universe possible. And that’s yet another reason why it keeps showing up. As far as what’s necessary to address hierarchy problems, it’s certainly not necessary there. There are other theoretical ideas that you could imagine, but it continues to be probably the most appealing one. As far as the mathematical structure of quantum field theory, hopefully it isn’t totally necessary. Hopefully we’ll discover amazing dynamics and mathematical structures in non-supersymmetric theories that look like they’re even going to be richer than the supersymmetric ones. But supersymmetry has been an absolutely indispensable tool—I cannot stress this enough—to start making progress.

From this point of view, the least-necessary aspect of it is the thing we hope to experimentally probe at the LHC. One should not take lightly the fact that so many different groups of theoretical physicists for the past 30 years keep running into this concept, over and over and over again. It’s thrust upon you from many different points of view. Although, having said that, if it is discovered at the LHC, it will be an absolute triumph. That would be glorious.

**Other than waiting for the LHC, what have you been working on that you find exciting, or what have other people been doing that you find exciting and wish you’d done first? **

Like I said, as far as more formal theory is concerned, an important and very exciting direction is really understanding from many different points of view the dynamics of good old-fashioned gauge theories—that they do extraordinary things we didn’t anticipate. A lot of it has been sitting under our noses for 60 years. It’s starting to be unearthed. I have a very strong feeling that this will be a really important direction for the next 10 or 20 years.

There’s a remarkable connection between some very deep ideas in mathematics that are starting to emerge. These are really startling connections between the dynamics of gauge theories and conjectures in mathematics that are related to the Reimann hypothesis. There’s always been a big confluence between math and physics, but this is heading it into a really, really remarkable direction. Before, the kind of confluences involved ideas that you might think have something to do with physics—in geometry and manifolds, not number theory. And yet I think we’re really beginning to see the glimmerings of an actual direction between these much more abstract mathematical ideas, which is just extraordinary. This is what I’m obsessed about now. I haven’t been this excited about physics in a very long time.

Nima Arkani-Hamed

Institute for Advance Study

Princeton, NJ

KEYWORDS: SUPERSYMMETRY, QUANTUM FIELD THEORIES, MAXIMALLY SUPERSYMMETRIC THEORIES, STANDARD MODEL, LARGE HADRON COLLIDER, LHC, HIGGS BOSON