The Cosmic Landscape (39 page)

But in both archives you will find that many of the papers have something to do with supersymmetry. Each camp has its own reasons for this. For the hep-th people, the reasons are mathematical. Supersymmetry leads to amazing simplifications for problems that are much too hard otherwise. Remember that in chapter 2 I explained that the cosmological constant is guaranteed to be zero if particles come in superpartner pairs. This is one of many mathematical miracles that occur in supersymmetric theories. I won’t describe them, but the main point is that supersymmetry so simplifies the mathematics of quantum field theory and String Theory that it allows theorists to know things that would otherwise be far beyond calculation. The real world may not be supersymmetric, but there may be interesting phenomena that can be studied with the aid of supersymmetry: phenomena that ordinarily would be far too hard for us to comprehend. An example is black holes. Every theory that includes the force of gravity will have black holes among the objects it describes. Black holes have very mysterious and paradoxical properties that we will come upon later in this book. Speculations about these paradoxes have been much too complicated to check in an ordinary theory. But, as if by magic, the existence of superpartners makes black holes easy to study. For the string theorist this simplification is essential. The mathematics of the theory as it is now practiced relies almost wholly on supersymmetry. Even many old questions about the quantum mechanics of quarks and gluons become easy if we add superpartners. The supersymmetric world is not the real world (at least in our pocket universe), but it is close enough to hold many lessons about elementary particles and gravity.

Although the ultimate aims of hep-phers and hep-thers may be the same, phenomenologists have a different immediate agenda from string theorists. Their goal is to use the older methods and sometimes the new ideas of String Theory to describe Laws of Physics as they would have been understood for most of the twentieth century. They are usually not trying to build a theory from some first principles, a theory that would be mathematically complete, nor are they expecting to discover the ultimate theory. Their interest in supersymmetry is as a possible approximate or broken symmetry of nature, something that can be discovered in future laboratory experiments. For them the most important discoveries would be of a whole family of new particles—the missing superpartners.

Broken symmetries, remember, are not perfect. In a perfect mirror, an object and its mirror image are identical except that left and right are interchanged, but in a funhouse mirror the symmetry is imperfect. It may be good enough to recognize the image of an object, but image and object are distorted versions of each other. The image of a thin man might be a fat man who, if he were real, would have twice the weight of his thin twin.

In the funhouse that we call our universe, the mathematical supersymmetry “mirror” that reflects each particle into its superpartner is badly distorted, so badly distorted that the superpartners are like a very fat image. If they exist at all, they are many times heavier—more massive—than the known particles. No superpartner has ever been discovered: not the electron’s mate or the photon’s or the quarks’. Does that mean that they don’t exist and that supersymmetry is an irrelevant mathematical game? Perhaps so, but it could also mean the distortion is enough to make the superpartners so heavy that they are beyond the reach of current particle accelerators. If for some reason the superpartners were all a bit too massive—a couple of hundred times the proton mass—they could not be discovered until the next round of accelerators is built.

The superpartners all have names similar to their ordinary twins. It’s not too hard to remember them if you know the rule. If the ordinary particle is a boson like the photon or the Higgs boson, then the name of the fermion twin is obtained by adding
ino.
Thus the photino, the Higgsino, the Zino, and the gluino. If, on the other hand, the original particle is a fermion, then you just add the letter s at the beginning: selectron, smuon, sneutrino, squark, and so on. This last rule has generated some of the ugliest words in the physicist’s vocabulary.

There is always a strong tendency to hope that new discoveries are “just around the corner.” If the superpartners fail to show up at a hundred times the mass of the proton, then estimates will be revised, and an accelerator will have to be built in order to discover them at a thousand proton masses. Or at ten thousand proton masses. But is it all wishful thinking and no more? I don’t think so. There is a deep puzzle about the Higgs particle to which supersymmetry may hold the key. The problem is closely connected with the “mother of all physics problems” as well as with the surprising weakness of gravity.

The same quantum jitters that can create an enormous vacuum energy can also have an effect on the masses of elementary particles. Here’s the reason. Suppose a particle is placed into the jittery vacuum. That particle will interact with the quantum fluctuations and disturb the way the vacuum jitters in the immediate vicinity of the particle. Some particles will damp the jittery behavior; others will increase it. The overall effect is to modify the energy due to the jitters. This change in the jitter energy, due to the presence of the particle, must be counted as part of its mass (remember E = mc
²
). A particularly violent example is the effect on the mass of the Higgs boson. Physicists know how to estimate the additional extra mass of the Higgs, and the result is almost as absurd as the estimate for the vacuum energy itself. The vacuum jitters in the neighborhood of the Higgs boson ought to add enough mass to the Higgs boson to make it as heavy as the Planck mass!

Why is this so problematic? Although theorists usually focus on the Higgs particle, the problem really infects all the elementary particles, with the exception of the photon and graviton. Any particle placed in a jittery vacuum will suffer an enormous increase in its mass. If all the particles had their masses increased, all matter would become heavier, and that would imply that the gravitational forces between objects would become stronger. It takes only a modest increase in the strength of gravity to render the world lifeless. This dilemma is conventionally called the Higgs mass problem and is another fine-tuning problem that belabors theorists’ attempts to understand the Laws of Physics. The two problems—the cosmological constant and the Higgs mass—are in many ways very similar. But what do they have to do with supersymmetry?

Remember that in chapter 2 I explained that an exact twinning of fermions and bosons would cancel the fluctuating energy of the vacuum. Exactly the same is true of the extra, unwanted mass of parti-cles. In a supersymmetric world the violent effects due to quantum fluctuations would be tamed, leaving the particle masses undisturbed. Moreover, even a distorted supersymmetry would alleviate the problem a great deal if the distortion were not too severe. This is the primary reason that elementary-particle physicists hope that supersymmetry is “just around the corner.” It should be noted, however, that distorted supersymmetry cannot account for the absurdly small value of the cosmological constant. It’s just too small.

The problem of the Higgs mass is similar to the problem of vacuum energy in another way. Just as Weinberg showed that life could not exist in a world with too much vacuum energy, heavier elementary particles would also be disastrous. Perhaps the explanation of the Higgs mass problem lies not in supersymmetry but rather in the enormous diversity of the Landscape and the anthropic need for the mass to be small. In a few years we may know whether supersymmetry really is just around the corner or if it is a mirage that keeps receding as we approach it.

One question that seems not to have been asked by theoretical physicists is: “If supersymmetry is such a wonderful, elegant, mathematical symmetry, why isn’t the world supersymmetric? Why don’t we live in the kind of elegant universe that string theorists know and love best?” Could the reason be anthropic?

The biggest threat to life in an exactly supersymmetric universe doesn’t have to do with cosmology but, rather, with chemistry. In a supersymmetric universe every fermion has a boson partner with exactly the same mass, and therein lies the trouble. The culprits are the superpartners of the electron and the photon. These two particles, called the selectron (ugh!) and the photino, conspire to destroy all ordinary atoms.

Take a carbon atom. The chemical properties of carbon depend primarily on the valence electrons—the most loosely bound electrons in the outermost orbits. But in a supersymmetric world, an outer electron can emit a photino and turn into a selectron. The massless photino flies off with the speed of light, leaving the selectron to replace the electron in the atom. That’s a big problem: the selectron, being a boson, is not blocked (by the Pauli exclusion principle) from dropping down to lower energy orbits near the nucleus. In a very short time, all the electrons will become selectrons trapped in the innermost orbit. Good-bye to the chemical properties of carbon—and every other molecule needed for life. A supersymmetric world may be very elegant, but it can’t support life—not of our kind, anyway.

If you go back to the physics archive Web site, you will find two other archives, one called General Relativity and Quantum Cosmology, the other Astrophysics. In these archives supersymmetry plays a much less prominent role. Why should a cosmologist pay any attention to supersymmetry if the world is not supersymmetric? To paraphrase Bill Clinton, “It’s the Landscape, stupid.” Although a particular symmetry may be broken to a greater or lesser degree in our little home valley, that doesn’t mean that the symmetry is broken in all corners of the Landscape. Indeed, the portion of the String Theory Landscape that we know most about is the region where supersymmetry is exact and unbroken. Called the
supersymmetric moduli space
(or supermoduli space), it is the portion of the Landscape where every fermion has its boson and every boson has its fermion. As a consequence, the vacuum energy is exactly zero everywhere on the supermoduli space. Topographically, that makes it a plain at exactly zero altitude. Most of what we know about String Theory comes from our thirty-five-year exploration of this plain. Of course this also implies that some pockets of the megaverse will be supersymmetric. But there are no superstring theorists to enjoy it.

By 1985 String Theory—now called superString Theory—had five distinct versions.
⁴
They differed in a number of ways. Two had open strings (strings with two ends) as well as closed strings—three did not. The names of the five are not particularly enlightening, but here they are. The two with open strings are called Type Ia and Ib String Theories. The remaining three with only closed strings are known as Type IIa, Type IIb, and Heterotic String Theories. The distinctions are too technical to describe without boring the reader. But one thing that they have in common is far more interesting than any of the differences: although some have open strings and some don’t, all five versions have closed strings.

To appreciate why this is so interesting, we need to understand a very disappointing failure of all previous theories. In ordinary theories—theories such as Quantum Electrodynamics or the Standard Model—gravity is an optional “add-on.” You can either ignore gravity or add it into the brew. The recipe is simple: take the Standard Model and add one more particle, the graviton. Let the graviton be massless. Also add some new vertices: any particle can emit a graviton. That’s it. But it doesn’t work very well. The mathematics is intricate and subtle, but at the end of the day, the new Feynman diagrams involving gravitons make hash out of the earlier calculations. Everything comes out infinite. There is no way to make sense of the theory.

In a way I think it is a good thing that the simple procedure failed. It contains no hint of an explanation of the properties of particles, it has no explanation of why the Standard Model is special, and it explains nothing about the fine-tuning of the cosmological constant or the Higgs mass. Frankly, if it worked, it would be very disappointing.

But the five String Theories are very clear on this point: they simply cannot be formulated without gravity. Gravity is not an arbitrary input—it is an inevitable outcome. String Theory, in order to be consistent,
must
include the graviton and the forces that it mediates by exchange. The reason is simple. The graviton is a closed string, the lightest one. Open strings are optional, but closed strings are always there. Suppose we try to create a theory with only open strings. If we succeed we will have a String Theory without gravity. But we will always fail. The two ends of an open string can always find each other and join to form a closed string. Ordinary theories are consistent
only
if gravity is left out. String Theory is consistent
only
if it includes gravity. That fact, more than any other, gives string theorists confidence that they are on the right track.

The four theories labeled Types I and II were first discovered in the 1970s. Each had fatal defects, not in their internal mathematical consistency, but in the detailed comparison with experimental facts about particles. Each described a possible world. They just did not describe our world. Thus, enormous excitement ensued when the fifth version was discovered in Princeton, in 1985. The Heterotic String Theory appeared to be the string theorist’s dream. It looked enough like the real world to perhaps be the real thing. Success was declared imminent.

Even then there were reasons to be suspicious of the strong claims. For one thing, there was still the problem of too many dimensions: nine of space and one of time. But theorists already knew what to do with the extra six dimensions: “Compactify!” they said. But there are millions of possible choices among Calabi Yau spaces. Moreover, every one of them gives a consistent theory. Even worse, once a Calabi Yau manifold was chosen, there were hundreds of moduli associated with its shape and size. These, too, had to be fixed by hand. Furthermore, the known theories were all supersymmetric: in each case the particles came in exactly matched pairs, which we know does not fit our reality.