Tag Archives: supersymmetry

The Road to Seven-Loop Supergravity

There’s an obvious way to put together a theory of quantum gravity. And it doesn’t work.

Do the same thing you would with any other theory, and you get infinity. You get repeated infinities, an infinity of infinities. And while you could fix one or two infinities, fixing an infinite number requires giving up an infinity of possible predictions, so in the end your theory predicts nothing.

String theory fixes this with its own infinity, the infinite number of ways a string can vibrate. Because this infinity is organized and structured and well-understood, you’re left with a theory that is still at least capable of making predictions.

(Note that this is an independent question from whether string theory can make predictions for experiments in the real world. This is a much more “in-principle” statement: if we knew everything we might want to about physics, all the fields and particles and shapes of the extra dimensions, we could use string theory to make predictions. Even if we knew all of that, we still couldn’t make predictions from naive quantum gravity.)

Are there ways to fix the problem that don’t involve an infinity of vibrations? Or at least, to fix part of the problem?

That’s what Zvi Bern, John Joseph Carrasco, Henrik Johansson, and a growing cast of collaborators have been trying to find out.

They’re investigating N=8 supergravity, a theory that takes gravity and adds on a host of related particles. It’s one of the easiest theories to get from string theory, by curling up extra dimensions in a particularly simple way and ignoring higher-energy vibrations.

Bern, along with Lance Dixon and David Kosower, invented the generalized unitarity technique I talked about last week. Along with Carrasco and Johansson, he figured out another important trick: the idea that you can do calculations in gravity by squaring the appropriate part of calculations in Yang-Mills theory. For N=8 supergravity, the theory you need to square is my favorite theory, N=4 super Yang-Mills.

Using this, they started pushing forward, calculating approximations to greater and greater precision (more and more loops).

What they found, at each step, was that N=8 supergravity behaved better than expected. In fact, it behaved like N=4 super Yang-Mills.

N=4 super Yang-Mills is special, because in four dimensions (three space and one time, the dimensions we’re used to in daily life) there are no infinities to fix. In a world with more dimensions, though, you start getting infinities, and with more and more loops you need fewer and fewer dimensions to see them.

N=8 supergravity, unexpectedly, was giving infinities in the same dimensions that N=4 super Yang-Mills did (and no earlier). If it kept doing that, you might guess that it also had no infinities in four dimensions. You might wonder if, at least loop by loop, N=8 supergravity could be a way to fix quantum gravity without string theory.

Of course, you’d only really know if you could check in four dimensions.

If you want to check in four dimensions, though, you run into a problem. The fewer dimensions you’re looking at, the more loops you need before N=8 supergravity could possibly give infinity. In four dimensions, you need a forbidding seven loops of precision.

(To compare, the highest precision of things we’ve actually tested in the real world is four loops.)

Still, Bern, Carrasco, and Johansson were up to the challenge. Along with Lance Dixon, David Kosower, and Radu Roiban, they looked at three loops, calculating an interaction of four gravitons, and the pattern continued. Four loops, and it was still going strong.

At around this time, I had just started grad school. My first project was a cumbersome numerical calculation. To keep me motivated, my advisor mentioned that the work I was doing would be good preparation for a much grander project: the calculation of whether the four-graviton interaction in N=8 supergravity diverges at seven loops. All I’d have to do was wait for Bern and collaborators to get there.

I named this blog “4 gravitons and a grad student”, and hoped I would get a chance to contribute.

And then something unexpected happened. They got stuck at five loops.

The method they were using, generalized unitarity, is an ansatz-based method. You start with a guess, then refine it. As such, the method is ultimately only as good as your guess.

Their guesses, in general, were pretty good. The trick they were using, squaring N=4 to get N=8, requires a certain type of guess: one in which the pieces they square have similar relationships to the different types of charge in Yang-Mills theory. There’s still an infinite number of guesses that can obey this, so they applied more restrictions, expectations based on other calculations, to get something more manageable. This worked at three loops, and worked (with a little extra thought) at four loops.

But at five loops they were stuck. They couldn’t find anything, with their restrictions, that gave the correct answer when “cut up” by generalized unitarity. And while they could drop some restrictions, if they dropped too many they’d end up with far too general a guess, something that could take months of computer time to solve.

So they stopped.

They did quite a bit of interesting work in the meantime. They found more theories they could square to get gravity theories, of more and more unusual types. They calculated infinities in other theories, and found surprises there too, other cases where infinities didn’t show up when they were “supposed” to. But for some time, the N=8 supergravity calculation was stalled.

And in the meantime, I went off in another direction, which long-time readers of this blog already know about.

Recently, though, they’ve broken the stall.

What they realized is that the condition on their guess, that the parts they square be related like Yang-Mills charges, wasn’t entirely necessary. Instead, they could start with a “bad” guess, and modify it, using the failure of those relations to fill in the missing pieces.

It looks like this is going to work.

We’re all at an amplitudes program right now in Santa Barbara. Walking through the halls of the KITP, I overhear conversations about five loops. They’re paring things down, honing their code, getting rid of the last few bugs, and checking their results.

They’re almost there, and it’s exciting. It looks like finally things are moving again, like the train to seven loops has once again left the station.

Increasingly, they’re beginning to understand the absent infinities, to see that they really are due to something unexpected and new.

N=8 supergravity isn’t going to be the next theory of everything. (For one, you can’t get chiral fermions out of it.) But if it really has no infinities at any loop, that tells us something about what a theory of quantum gravity is allowed to be, about the minimum necessary to at least make sense on a loop-by-loop level.

And that, I think, is worth being excited about.

Poll Results, and What’s Next

I’ll leave last week’s poll up a while longer as more votes trickle in, but the overall pattern (beyond “Zipflike“) is pretty clear.

From pretty early on, most requests were for more explanations of QFT, gravity, and string theory concepts, with amplitudes content a clear second. This is something I can definitely do more of: I haven’t had much inspiration for interesting pieces of this sort recently, but it’s something I can ramp up in future.

I suspect that many of the people voting for more QFT and more amplitudes content were also interested in something else, though: more physics news. Xezlec mentioned that with Résonaances and Of Particular Significance quiet, there’s an open niche for vaguely reasonable people blogging about physics.

The truth is, I didn’t think of adding a “more physics news” option to the poll. I’m not a great source of news: not being a phenomenologist, I don’t keep up with the latest experimental results, and since my sub-field is small and insular I’m not always aware of the latest thing Witten or Maldacena is working on.

For an example of the former: recently, various LHC teams presented results at the Moriond and Aspen conferences, with no new evidence of supersymmetry in the data they’ve gathered thus far. This triggered concessions on several bets about SUSY (including an amusingly awkward conversation about how to pay one of them).

And I only know about that because other bloggers talked about it.

So I’m not going to be a reliable source of physics news.

With that said, knowing there’s a sizable number of people interested in this kind of thing is helpful. I’ve definitely had times when I saw something I found interesting, but wasn’t sure if my audience would care. (For example, recently there’s been some substantial progress on the problem that gave this blog its name.) Now that I know some of you are interested, I’ll err on the side of posting about these kinds of things.

“What’s it like to be a physicist” and science popularization were both consistently third and fourth in the poll, switching back and forth as more votes came in. This tells me that while many of you want more technical content, there are still people interested in pieces aimed to a broader audience, so I won’t abandon those.

The other topics were fairly close together, with the more “news-y” ones (astrophysics/cosmology and criticism of bad science coverage) beating the less “news-y” ones. This also supports my guess that people were looking for a “more physics news” option. A few people even voted for “more arguments”, which was really more of a joke topic: getting into arguments with other bloggers tends to bring in readers, but it’s not something I ever plan to do intentionally.

So, what’s next? I’ll explain more quantum field theory, talk more about interesting progress in amplitudes, and mention news when I come across it, trusting you guys to find it interesting. I’ll keep up with the low-level stuff, and with trying to humanize physics, to get the public to understand what being a physicist is all about. And I’ll think about some of the specific suggestions you gave: I’m always looking for good post ideas.

The Parable of the Entanglers and the Bootstrappers

There’s been some buzz around a recent Quanta article by K. C. Cole, The Strange Second Life of String Theory. I found it a bit simplistic of a take on the topic, so I thought I’d offer a different one.

String theory has been called the particle physicist’s approach to quantum gravity. Other approaches use the discovery of general relativity as a model: they’re looking for a big conceptual break from older theories. String theory, in contrast, starts out with a technical problem (naive quantum gravity calculations that give infinity) proposes physical objects that could solve the problem (strings, branes), and figures out which theories of these objects are consistent with existing data (originally the five superstring theories, now all understood as parts of M theory).

That approach worked. It didn’t work all the way, because regardless of whether there are indirect tests that can shed light on quantum gravity, particle physics-style tests are far beyond our capabilities. But in some sense, it went as far as it can: we’ve got a potential solution to the problem, and (apart from some controversy about the cosmological constant) it looks consistent with observations. Until actual evidence surfaces, that’s the end of that particular story.

When people talk about the failure of string theory, they’re usually talking about its aspirations as a “theory of everything”. String theory requires the world to have eleven dimensions, with seven curled up small enough that we can’t observe them. Different arrangements of those dimensions lead to different four-dimensional particles. For a time, it was thought that there would be only a few possible arrangements: few enough that people could find the one that describes the world and use it to predict undiscovered particles.

That particular dream didn’t work out. Instead, it became apparent that there were a truly vast number of different arrangements of dimensions, with no unique prediction likely to surface.

By the time I took my first string theory course in grad school, all of this was well established. I was entering a field shaped by these two facts: string theory’s success as a particle-physics style solution to quantum gravity, and its failure as a uniquely predictive theory of everything.

The quirky thing about science: sociologically, success and failure look pretty similar. Either way, it’s time to find a new project.

A colleague of mine recently said that we’re all either entanglers or bootstrappers. It was a joke, based on two massive grants from the Simons Foundation. But it’s also a good way to summarize two different ways string theory has moved on, from its success and from its failure.

The entanglers start from string theory’s success and say, what’s next?

As it turns out, a particle-physics style understanding of quantum gravity doesn’t tell you everything you need to know. Some of the big conceptual questions the more general relativity-esque approaches were interested in are still worth asking. Luckily, string theory provides tools to answer them.

Many of those answers come from AdS/CFT, the discovery that string theory in a particular warped space-time is dual (secretly the same theory) to a more particle-physics style theory on the edge of that space-time. With that discovery, people could start understanding properties of gravity in terms of properties of particle-physics style theories. They could use concepts like information, complexity, and quantum entanglement (hence “entanglers”) to ask deeper questions about the structure of space-time and the nature of black holes.

The bootstrappers, meanwhile, start from string theory’s failure and ask, what can we do with it?

Twisting up the dimensions of string theory yields a vast number of different arrangements of particles. Rather than viewing this as a problem, why not draw on it as a resource?

“Bootstrappers” explore this space of particle-physics style theories, using ones with interesting properties to find powerful calculation tricks. The name comes from the conformal bootstrap, a technique that finds conformal theories (roughly: theories that are the same at every scale) by “pulling itself by its own boostraps”, using nothing but a kind of self-consistency.

Many accounts, including Cole’s, attribute people like the boostrappers to AdS/CFT as well, crediting it with inspiring string theorists to take a closer look at particle physics-style theories. That may be true in some cases, but I don’t think it’s the whole story: my subfield is bootstrappy, and while it has drawn on AdS/CFT that wasn’t what got it started. Overall, I think it’s more the case that the tools of string theory’s “particle physics-esque approach”, like conformal theories and supersymmetry, ended up (perhaps unsurprisingly) useful for understanding particle physics-style theories.

Not everyone is a “boostrapper” or an “entangler”, even in the broad sense I’m using the words. The two groups also sometimes overlap. Nevertheless, it’s a good way to think about what string theorists are doing these days. Both of these groups start out learning string theory: it’s the only way to learn about AdS/CFT, and it introduces the bootstrappers to a bunch of powerful particle physics tools all in one course. Where they go from there varies, and can be more or less “stringy”. But it’s research that wouldn’t have existed without string theory to get it started.

Particles Aren’t Vibrations (at Least, Not the Ones You Think)

You’ve probably heard this story before, likely from Brian Greene.

In string theory, the fundamental particles of nature are actually short lengths of string. These strings can vibrate, and like a string on a violin, that vibration is arranged into harmonics. The more energy in the string, the more complex the vibration. In string theory, each of these vibrations corresponds to a different particle, explaining how the zoo of particles we observe can come out of a single type of fundamental string.


Particles. Probably.

It’s a nice story. It’s even partly true. But it gives a completely wrong idea of where the particles we’re used to come from.

Making a string vibrate takes energy, and that energy is determined by the tension of the string. It’s a lot harder to wiggle a thick rubber band than a thin one, if you’re holding both tightly.

String theory’s strings are under a lot of tension, so it takes a lot of energy to make them vibrate. From our perspective, that energy looks like mass, so the more complicated harmonics on a string correspond to extremely massive particles, close to the Planck mass!

Those aren’t the particles you’re used to. They’re not electrons, they’re not dark matter. They’re particles we haven’t observed, and may never observe. They’re not how string theory explains the fundamental particles of nature.

So how does string theory go from one fundamental type of string to all of the particles in the universe, if not through these vibrations? As it turns out, there are several different ways it can happen, tricks that allow the lightest and simplest vibrations to give us all the particles we’ve observed.* I’ll describe a few.

The first and most important trick here is supersymmetry. Supersymmetry relates different types of particles to each other. In string theory, it means that along with vibrations that go higher and higher, there are also low-energy vibrations that behave like different sorts of particles. In a sense, string theory sticks a quantum field theory inside another quantum field theory, in a way that would make Xzibit proud.

Even with supersymmetry, string theory doesn’t give rise to all of the right sorts of particles. You need something else, like compactifications or branes.

The strings of string theory live in ten dimensions, it’s the only place they’re mathematically consistent. Since our world looks four-dimensional, something has to happen to the other six dimensions. They have to be curled up, in a process called compactification. There are lots and lots (and lots) of ways to do this compactification, and different ways of curling up the extra dimensions give different places for strings to move. These new options make the strings look different in our four-dimensional world: a string curled around a donut hole looks very different from one that moves freely. Each new way the string can move or vibrate can give rise to a new particle.

Another option to introduce diversity in particles is to use branes. Branes (short for membranes) are surfaces that strings can end on. If two strings end on the same brane, those ends can meet up and interact. If they end on different branes though, then they can’t. By cleverly arranging branes, then, you can have different sets of strings that interact with each other in different ways, reproducing the different interactions of the particles we’re familiar with.

In string theory, the particles we’re used to aren’t just higher harmonics, or vibrations with more and more energy. They come from supersymmetry, from compactifications and from branes. The higher harmonics are still important: there are theorems that you can’t fix quantum gravity with a finite number of extra particles, so the infinite tower of vibrations allows string theory to exploit a key loophole. They just don’t happen to be how string theory gets the particles of the Standard Model. The idea that every particle is just a higher vibration is a common misconception, and I hope I’ve given you a better idea of how string theory actually works.


*But aren’t these lightest vibrations still close to the Planck mass? Nope! See the discussion with TE in the comments for details.

Living in a Broken World: Supersymmetry We Can Test

I’ve talked before about supersymmetry. Supersymmetry relates particles with different spins, linking spin 1 force-carrying particles like photons and gluons to spin 1/2 particles similar to electrons, and spin 1/2 particles in turn to spin 0 “scalar” particles, the same general type as the Higgs. I emphasized there that, if two particles are related by supersymmetry, they will have some important traits in common: the same mass and the same interactions.

That’s true for the theories I like to work with. In particular, it’s true for N=4 super Yang-Mills. Adding supersymmetry allows us to tinker with neater, cleaner theories, gaining mastery over rice before we start experimenting with the more intricate “sushi” of theories of the real world.

However, it should be pretty clear that we don’t live in a world with this sort of supersymmetry. A quick look at the Standard Model indicates that no two known particles interact in precisely the same way. When people try to test supersymmetry in the real world, they’re not looking for this sort of thing. Rather, they’re looking for broken supersymmetry.

In the past, I’ve described broken supersymmetry as like a broken mirror: the two sides are no longer the same, but you can still predict one side’s behavior from the other. When supersymmetry is broken, related particles still have the same interactions. Now, though, they can have different masses.

The simplest version of supersymmetry, N=1, gives one partner to each particle. Since nothing in the Standard Model can be partners of each other, if we have broken N=1 supersymmetry in the real world then we need a new particle for each existing one…and each one of those particles has a potentially unknown, different mass. And if that sounds rather complicated…

Baroque enough to make Rubens happy.

That, right there, is the Minimal Supersymmetric Standard Model, the simplest thing you can propose if you want a world with broken supersymmetry. If you look carefully, you’ll notice that it’s actually a bit more complicated than just one partner for each known particle: there are a few extra Higgs fields as well!

If we’re hoping to explain anything in a simpler way, we seem to have royally screwed up. Luckily, though, the situation is not quite as ridiculous as it appears. Let’s go back to the mirror analogy.

If you look into a broken mirror, you can still have a pretty good idea of what you’ll see…but in order to do so, you have to know how the mirror is broken.

Similarly, supersymmetry can be broken in different ways, by different supersymmetry-breaking mechanisms.

The general idea is to start with a theory in which supersymmetry is precisely true, and all supersymmetric partners have the same mass. Then, consider some Higgs-like field. Like the Higgs, it can take some constant value throughout all of space, forming a background like the color of a piece of construction paper. While the rules that govern this field would respect supersymmetry, any specific value it takes wouldn’t. Instead, it would be biased: the spin 0, Higgs-like field could take on a constant value, but its spin 1/2 supersymmetric partner couldn’t. (If you want to know why, read my post on the Higgs linked above.)

Once that field takes on a specific value, supersymmetry is broken. That breaking then has to be communicated to the rest of the theory, via interactions between different particles. There are several different ways this can work: perhaps the interactions come from gravity, or are the same strength as gravity. Maybe instead they come from a new fundamental force, similar to the strong nuclear force but harder to discover. They could even come as byproducts of the breaking of other symmetries.

Each one of these options has different consequences, and leads to different predictions for the masses of undiscovered partner particles. They tend to have different numbers of extra parameters (for example, if gravity-based interactions are involved there are four new parameters, and an extra sign, that must be fixed). None of them have an entire standard model-worth of new parameters…but all of them have at least a few extra.

(Brief aside: I’ve been talking about the Minimal Supersymmetric Standard Model, but these days people have largely given up on finding evidence for it, and are exploring even more complicated setups like the Next-to-Minimal Supersymmetric Standard Model.)

If we’re introducing extra parameters without explaining existing ones, what’s the point of supersymmetry?

Last week, I talked about the problem of fine-tuning. I explained that when physicists are worried about fine-tuning, what we’re really worried about is whether the sorts of ultimate (low number of parameters) theories that we expect to hold could give rise to the apparently fine-tuned world we live in. In that post, I was a little misleading about supersymmetry’s role in that problem.

The goal of introducing (broken) supersymmetry is to solve a particular set of fine-tuning problems, mostly one specific one involving the Higgs. This doesn’t mean that supersymmetry is the sort of “ultimate” theory we’re looking for, rather supersymmetry is one of the few ways we know to bridge the gap between “ultimate” theories and a fine-tuned real world.

To explain it in terms of the language of the last post, it’s hard to find one of these “ultimate” theories that gives rise to a fine-tuned world. What’s quite a bit easier, though, is finding one of these “ultimate” theories that gives rise to a supersymmetric world, which in turn gives rise to a fine-tuned real world.

In practice, these are the sorts of theories that get tested. Very rarely are people able to propose testable versions of the more “ultimate” theories. Instead, one generally finds intermediate theories, theories that can potentially come from “ultimate” theories, and builds general versions of those that can be tested.

These intermediate theories come in multiple levels. Some physicists look for the most general version, theories like the Minimal Supersymmetric Standard Model with a whole host of new parameters. Others look for more specific versions, choices of supersymmetry-breaking mechanisms. Still others try to tie it further up, getting close to candidate “ultimate” theories like M theory (though in practice they generally make a few choices that put them somewhere in between).

The hope is that with a lot of people covering different angles, we’ll be able to make the best use of any new evidence that comes in. If “something” is out there, there are still a lot of choices for what that something could be, and it’s the job of physicists to try to understand whatever ends up being found.

Not bad for working in a broken world, huh?

The Real Problem with Fine-Tuning

You’ve probably heard it said that the universe is fine-tuned.

The Standard Model, our current best understanding of the rules that govern particle physics, is full of lots of fiddly adjustable parameters. The masses of fundamental particles and the strengths of the fundamental forces aren’t the sort of thing we can predict from first principles: we need to go out, do experiments, and find out what they are. And you’ve probably heard it argued that, if these fiddly parameters were even a little different from what they are, life as we know it could not exist.

That’s fine-tuning…or at least, that’s what many people mean when they talk about fine-tuning. It’s not exactly what physicists mean though. The thing is, almost nobody who studies particle physics thinks the parameters of the Standard Model are the full story. In fact, any theory with adjustable parameters probably isn’t the full story.

It all goes back to a point I made a while back: nature abhors a constant. The whole purpose of physics is to explain the natural world, and we have a long history of taking things that look arbitrary and linking them together, showing that reality has fewer parameters than we had thought. This is something physics is very good at. (To indulge in a little extremely amateurish philosophy, it seems to me that this is simply an inherent part of how we understand the world: if we encounter a parameter, we will eventually come up with an explanation for it.)

Moreover, at this point we have a rough idea of what this sort of explanation should look like. We have experience playing with theories that don’t have any adjustable parameters, or that only have a few: M theory is an example, but there are also more traditional quantum field theories that fill this role with no mention of string theory. From our exploration of these theories, we know that they can serve as the kind of explanation we need: in a world governed by one of these theories, people unaware of the full theory would observe what would look at first glance like a world with many fiddly adjustable parameters, parameters that would eventually turn out to be consequences of the broader theory.

So for a physicist, fine-tuning is not about those fiddly parameters themselves. Rather, it’s about the theory that predicts them. Because we have experience playing with these sorts of theories, we know roughly the sorts of worlds they create. What we know is that, while sometimes they give rise to worlds that appear fine-tuned, they tend to only do so in particular ways. Setups that give rise to fine-tuning have consequences: supersymmetry, for example, can give rise to an apparently fine-tuned universe but has to have “partner” particles that show up in powerful enough colliders. In general, a theory that gives rise to apparent fine-tuning will have some detectable consequences.

That’s where physicists start to get worried. So far, we haven’t seen any of these detectable consequences, and it’s getting to the point where we could have, had they been the sort many people expected.

Physicists are worried about fine-tuning, but not because it makes the universe “unlikely”. They’re worried because the more finely-tuned our universe appears, the harder it is to find an explanation for it in terms of the sorts of theories we’re used to working with, and the less likely it becomes that someone will discover a good explanation any time soon. We’re quite confident that there should be some explanation, hundreds of years of scientific progress strongly suggest that to be the case. But the nature of that explanation is becoming increasingly opaque.

N=8: That’s a Whole Lot of Symmetry

In two weeks, I’m planning an extensive overhaul of the blog. I’ll be switching from 4gravitons.wordpress.com to just 4gravitons.wordpress.com, since I’m no longer a grad student. Don’t worry, I’ll be forwarding traffic from the old address, so if you miss the changeover you’ll have plenty of time to readjust. I’ll also be changing the blog’s look a bit, and adding some new tools and sections, including my current project, a series on the theory N=8 supergravity. This is post will be the last in the N=8 supergravity series.

I’ve told you about how gravity can be thought of as interactions with spin 2 particles, called gravitons. I’ve talked about how adding supersymmetry gives you a whole new type of particle, a gravitino, one different from all of the other particles we’ve seen in nature. Add supersymmetry to gravity, and you get a type of theory called supergravity.

In this post I want to discuss a particularly interesting form of supergravity. It’s called N=8 supergravity, and it’s closely related to N=4 super Yang-Mills.

In my articles about N=4 super Yang-Mills, I talked about supersymmetry. Supersymmetry is a relationship between particles of spin X and particles of spin X-½, but it gets more complicated when N (the number of “directions” of supersymmetry) is greater than one.

I’d encourage you to read at least the two links in the above paragraph. The gist is that just like a symmetrical object can be turned in different directions and still remain the same, a supersymmetrical theory can be “turned” so that a particle with spin X becomes a particle of spin X-½ (a different type of particle), and the theory will remain the same. The higher the number N, the more different directions the theory can be “turned”.

N=4 was something I could depict in a picture. We started with a particle of spin 1, then could “turn” it in four different directions, each resulting in a different particle of spin ½. By combining two different “turns” we ended up with six distinct particles of spin 0. Miraculously, I could fit this all into one image.

N=8 is tougher. This time, we start with 1 particle of spin 2: the graviton, the particle that corresponds to the force of gravity. From there we can “turn” the theory in eight different directions, leading to 8 different gravitino particles with spin 3/2.

After that, things get more complicated. You can “turn” the theory twice to reach spin 1. Spin 1 particles correspond to Yang-Mills forces, the fundamental forces of nature (besides gravity). Photons are the spin 1 particles that correspond to Electromagnetism. The spin 1 particles here, connected as they are to gravity by supersymmetry, are typically called graviphotons. There are 28 distinct graviphotons in N=8 supergravity.

From the graviphotons, we can keep turning, getting to spin ½, where we find 56 new particles of the same “type” as electrons and quarks. On our fourth turn, we get to spin 0, the scalars, with 70 new particles. Turning further takes us back: from spin 0 to spin ½, spin ½ to spin 1, spin 1 to spin 3/2, and spin 3/2 to spin 2, back where we started after eight “turns”.

I’ve tried to depict this in the same way as N=4 super Yang-Mills, but there’s just no way to fit everything in. The best I can do is to take a slice through the space, letting certain particles overlap to give at best a general impression of what’s going on.

Graviton in black, gravitinos in grey, graviphotons in yellow, fermions in orange, scalars in red, and comprehensibility omitted entirely.

Graviton in black, gravitinos in grey, graviphotons in yellow, fermions in orange, scalars in red, making a firework of incomprehensible graphics. Incidentally, happy 4th of July to my American readers.

That picture doesn’t give you any intuition about the numbers. It doesn’t show you why there are 28 graviphotons, or 70 scalars. To explain that, it’s best to turn to another, hopefully more familiar picture, Pascal’s triangle.

Getting math class flashbacks yet?

Pascal’s triangle is a way of writing down how many distinct combinations you can make out of a list, and that’s really all that’s going on here. If you have four directions to “turn” and you pick one, you have four options, while picking two gives you six distinct choices. That’s just the 1-4-6-4-1 line on the triangle. If you go down to the eighth, you’ll spot the numbers from N=8 supergravity: 1 graviton, 8 gravitinos, 28 graviphotons, 56 fermions, and 70 scalars.

That’s a lot of particles. With that many particles, you might wonder if you could somehow fit the real world in there.

Actually, that isn’t such a naive thought. When N=8 supergravity was first discovered, people tried to fit the existing particles of nature inside it, hoping that it could explain them. Over the years though, it was realized that N=8 supergravity simply doesn’t provide enough tools to fully capture the particles of the standard model. Something more diverse, like string theory, would be needed.

That means that N=8 supergravity, like many of the things theorists call theories, does not describe the real world. Instead, it’s interesting for a different reason.

You’ve probably heard that gravity and quantum mechanics are incompatible. That’s not exactly true: you can write down a quantum theory of gravity about as easily as you can write down a quantum theory of anything else. The problem is that most such theories have divergences, infinite results that shouldn’t be infinite. Dealing with those results involves a process called renormalization, which papers over the infinities but reduces our ability to make predictions. For gravity theories, this process has to be performed an infinite number of times, resulting in an infinite loss of predictability. So while you can certainly write down a theory of quantum gravity, you can’t predict anything with it.

String theory is different. It doesn’t have the same sorts of infinite results, doesn’t require renormalization. That, really, is it’s purpose, it’s biggest virtue: everything else is a side benefit.

N=4 super Yang-Mills isn’t a theory of gravity at all, but it does have that same neat trait: you never get this sort of infinite results, so you never need to give up predictive power.

What’s so cool about N=8 supergravity is that it just might be in the same category. By all rights, it shouldn’t be…but loop after loop its divergences seem to be behaving much like N=4 super Yang-Mills. (For those new to this blog, loops are a measure of how complex a calculation is in particle physics. Most practical calculations only involve one or two loops, while four loops represents possibly the most precise test ever performed by science.)

Now, two predictions are at the fore. One suggests that this magic behavior will be broken at the terrifyingly complex level of seven loops. The other proposes that the magic will continue, and N=8 supergravity will never see a divergence. The only way for certain is to do the calculation, look at four gravitons at seven loops and see what happens.

If N=8 supergravity really doesn’t diverge, then the biggest “point” of string theory isn’t unique anymore. If you don’t need all the bells and whistles of string theory to get an acceptable quantum theory of gravity, then maybe there’s a better way to think about the problem of quantum gravity in general. Even if N=8 supergravity doesn’t describe the real world, there may be other ways forward, other ways to handle the problem of divergences. If someone can manage that calculation (not as impossible as it sounds nowadays, but still very very hard) then we might see something really truly new.