In String Theory

Matter Particles and Force Particles
More examples could be given but this is enough to make the point. Now let me turn at last to what supersymmetry and string theory are. All particles do is interact. The Standard Model description of how they interact starts with the electron and quarks feeling the various forces, as described above. We know that magnets are surrounded by magnetic fields. Similarly, all particles are surrounded by gravitational fields, electrical fields and by the weak and strong force fields.

Particles feel the forces by "sensing" these fields. As quantum theory shows us, the effects of the forces are transmitted in chunks, quanta. The chunk, or quantum, of the electromagnetic field is the photon, and there are similar quanta for the other fields.

Thus our description is truly a particle one: there are matter particles that interact, and they do so by exchanging photons and other quanta of the fields.

The Symmetric 'Superpartners'
This description works very well. But it is an asymmetric one, with one type of particle as matter, another type as the particles mediating the forces. Supersymmetry is the idea that at a deeper level the laws of nature are more symmetric, that associated with each matter particle there is a previously unknown force particle, and associated with each force particle there is a previously unknown matter particle. These predicted particles are called superpartners.

Illustration by Sidney Harris for Supersymmetry by G. Kane

The equations that describe the hypothetical superpartners and their properties have led to new explanations and predictions. The most dramatic prediction is that the superpartners must exist—that they are real particles that physicists should be able to produce with colliding beams of particles.

If our understanding of the theory is basically correct, the new particles should be found at the upgraded facility at Fermi National Accelerator Laboratory, just west of Chicago. Fermilab will begin to take data in March 2001 after six years of improving the intensity and energy of the beams (and also upgrading the detectors needed to record the results of the collisions). Experimenters from the University of Michigan are among the leaders of these experiments.

Why do we call this property of the theory a symmetry, and why is it "super"? Scientists speak of a symmetry whenever the theory that describes a system doesn't change even if one modifies some of the terms in the equations that represent the theory. Here the symmetry is between the matter-type and force-type particles. They used the term "super" because the possibility of such a symmetry surprised them and because it had remarkable consequences.

The Score Calls for Strings
What is string theory? The Standard Model, and supersymmetry, too, are theories written in three space dimensions, with point-like particles. One problem with that approach became obvious in the 1970s, namely there did not seem to be any way to make a theory of gravity that was consistent with quantum theory and its chunks.

Einstein's theory of gravity was not a quantum theory, and physicists have understood that it would have to be extended, but there did not seem to be a way to do that. A few people realized that one could not make a consistent quantum theory of gravity if one tried to do it in three dimensions—height, width and depth—but that it was possible if the universe really has a larger number of dimensions.

Now we have learned that it is possible to make a quite remarkable theory in nine space dimensions. It seems to be consistent with the rules of quantum theory, to contain both gravity and the supersymmetric Standard Model, and to require only the forces that have been observed. In this theory the particles are the same ones we know—the particles of the Standard Model and their superpartners-but they are represented not as point—like quanta of fields but as tiny vibrating strings, so tiny they would appear point-like in any experiment we could do. They are not strings of anything; if they were, then that stuff would be more basic than the particles of the Standard Model. When we say they are strings, we mean their behavior is described by the same kinds of equations that would describe idealized everyday strings-thus, "string theory." Different patterns of vibration of the strings—the sort of changes that produce different notes from vibrating violin strings—correspond to different particles.

How can we think of our world as having extra dimensions? Mathematically, that's not very hard. But it is difficult to picture. Imagine that you can move only in two dimensions, length and width, of a big room, and that the third dimension, height, isn't large like the other two but curled up at each point in a tiny circle, so that you don't experience it. We don't yet know how the "extra" six dimensions are arranged—when we have learned that, perhaps it will be possible to provide a better picture.

Adagio for Five Strings in M
During the 1980s, as people studied string theory they realized that there seemed to be not one unique string theory as was hoped for if string theory were to be the most fundamental theory, but five different string theories plus a related theory called supergravity. That led to considerable discouragement with the whole approach.

Then in 1995 Edward Witten argued and presented evidence for the idea that there was in fact one primary theory. Supergravity and the five string theories were how this primary theory appeared if one looked at the primary theory from various limits or perspectives. He called the primary theory M-theory, and remarked that he wasn't sure if M stood for Mystery or Magic or Mother. And he drew the six-pointed figure shown here, with M-theory in the center and the various forms of string theory or supergravity represented by points on the edge. (More recently, we have realized that M of course stood for Michigan—this figure will be the logo of the international strings meeting being held here.)

String theory is very beautiful. It passes many tests by being consistent with gravity and quantum theory, and containing the Standard Model and the associated particles. But since it is formulated in nine space dimensions, not three, we can't tell if it really is the theory that describes our world. There are various ways the extra dimensions could hide. For example, they could be very tiny, so we could not move into them. Physicists describe this by saying the nine are "compacted" into our three.

There is another barrier to testing string theory. The world we live in is not fully supersymmetric. If it were, we would have known, to give one example, about another particle similar to the electron (that is, the electron's superpartner) for many years now, because it would be as ubiquitous as electrons. We expect to find evidence for a "broken" or partially hidden symmetry in comparison with what theory calls for. Once we have direct experimental detection of superpartners, understanding how supersymmetry is broken will become the central problem of the field.

In science, when a theory has symmetries there are implications for how the particles and systems decribed by the theory can behave. When symmetries are "broken," implications don't just go away, but they do change a little. For supersymmetry the key difference is that the superpartner particles should be heavier than their Standard Model partners. But the string theory calls for unbroken supersymmetry. So to test string theory we must learn both how to compactify the dimensions and also how its supersymmetry is broken. These are unsolved problems and very difficult ones.

I believe that they are too hard for solution by pure theoretical analysis and will yield only when we have considerable experimental data on the superpartners and their properties, data that point the way to both how supersymmetry is broken and how the extra dimensions are hidden. That is the historical path physics has followed as an experimental science, and I expect it to be followed here too.

Supersymmetry physics will be crucial to this quest. It is what connects the experimental data to the string theory. Experiment and string theory cannot talk to each other directly, but they can both communicate via supersymmetry.

A Melody Like Cake
I am often asked what is the connection between string theory and supersymmetry. String theory is like a musical score. Supersymmetry is like the performance. If you can read the score and hear it in your head you don't need the performance, but most of us do. Or, string theory is the recipe, supersymmetry is the cake.

If all goes as hoped, superpartners and Higgs bosons will be discovered, and their properties studied in detail, over the next 10 to 20 years. We are finally getting some of the facilities needed to do that, and we physicists hope that once the superpartners are found, the rest of the needed facilities will come.

The collider (called LEP) at the CERN laboratory in Geneva has just entered the region where the superpartners and Higgs boson could be found. Exploring this region requires two conditions: more energy in the colliding beams, to produce the expected heavier particles; and beams of large enough intensity to increase the frequency of collisions that produce new particles so they occur often enough to provide a convincing signal. Fermilab in Illinois will cover a major part of the region in the period 2001-2006, and further facilities will cover more of the region after that.

Of course things don't always go as hoped, and we cannot be certain of these breakthroughs. In the development of the Standard Model in the 1965-1980 period, the understanding reached a certain stage and then the experimental and theoretical progress came fast and the results fell into place as expected. In many ways we are in a similar situation today, and it is fair to hope for similar success. Then we will better understand this place where thunder and lightning and springtime and physicists and other people exist.

Gordon Kane, professor of physics, has written books for nonexperts on science, including The Particle Garden (Helix Books, 1995, hardcover, $22) and Supersymmetry: Unveiling the Ultimate Laws of Nature (Helix Books, 2000, hardcover, $26.)

The University of Michigan will host the annual international string theory meeting July 10-15, 2000. We expect over 350 string theorists from around the world to come. (More about the meeting can be learned from its web site http://feynman.physics.lsa.umich.edu/strings2000/) In the 1980s, Michigan physicists pioneered in a related area of physics called supersymmetry. The University hosted the annual international supersymmetry meeting in 1994. This year, that meeting will be at the large European center for particle physics, CERN, in Geneva, Switzerland, two weeks before the string theory meeting.—GK.