Warped Passages (46 page)

Even so, string theory was largely ignored until 1984, the year that Green and Schwarz demonstrated a startling feature of the superstring which convinced many other physicists that they were on a promising track. This discovery, together with two other developments that we’ll get to soon, are what put string theory into the mainstream of physics.

Green and Schwarz’s work addressed a phenomenon known as
anomalies
. As the name suggests, anomalies came as a big surprise
when they were first discovered. The first physicists who worked on quantum field theory took for granted that any symmetry of a classical theory would also be preserved by its quantum mechanical extension—the more comprehensive version of the theory that also includes the effects of virtual particles. But that is not always the case. In 1969, Steven Adler, John Bell, and Roman Jackiw showed that even when a classical theory preserves a symmetry, quantum mechanical processes involving virtual particles sometimes violate that symmetry. Such symmetry violations are called
anomalies
, and the theories that contain anomalies are labeled
anomalous
.

Anomalies are extremely relevant to the theories of forces. In Chapter 9 we saw that a successful theory of forces requires the existence of an internal symmetry. These symmetries must be exact, or else there’s no way to eliminate the unwanted polarization of the gauge boson, and the theory of forces will then make no sense. The symmetry associated with a force must therefore be
anomaly-free
—the sum of all symmetry-breaking effects must be zero.

This is a powerful constraint on any quantum theory of forces. For example, we now know that it is one of the most compelling explanations for the existence of both quarks and leptons in the Standard Model. Individually, virtual quarks and leptons would lead to anomalous quantum contributions that would break the symmetries of the Standard Model. However, the sum of the quantum contributions from the quarks and the leptons adds up to zero. This miraculous cancellation is what makes the Standard Model hold together; both leptons and quarks are necessary if the forces of the Standard Model are to make sense.

Anomalies were potentially a problem for string theory, which, after all, includes forces. In 1983, when the theorists Luis Alvarez-Gaume and Edward Witten showed that such anomalies occur not only in quantum field theory but also in string theory, it looked as if this discovery would consign string theory to the annals of interesting but overly far-reaching ideas. String theory didn’t seem as if it would preserve the requisite symmetries. In the skeptical environment created by string theory’s potential for anomalies, Green and Schwarz made quite a splash when they showed that string theory could satisfy the constraints that were needed to avoid anomalies. They computed the
quantum contribution to all possible anomalies and showed that for particular forces, anomalies would miraculously add up to zero.

One of the things that made Green and Schwarz’s result so surprising is that string theory allows many worrisome quantum mechanical processes, each of which looks as if it could create symmetry-breaking anomalies. But Green and Schwarz showed that the sum of the quantum mechanical contributions to all these possible symmetry-breaking anomalies in ten-dimensional superstring theory is zero. This meant that the many cancellations that were required in string theory calculations actually occur, and, furthermore, that the cancellations happen in ten dimensions, the number of dimensions that was already known to be special for superstring theory. This discovery was sufficiently miraculous for many physicists to decide that such conspiracies could not be coincidental. Anomaly cancellation was a powerful argument in favor of the ten-dimensional superstring.

Furthermore, Green and Schwarz completed their work at a felicitous moment. Physicists had been searching unsuccessfully for theories that could extend the Standard Model to incorporate supersymmetry and gravity, and they were ready to consider something new. They could not ignore Green and Schwarz’s discovery of a supersymmetric theory that could potentially reproduce all the particles and forces of the Standard Model. Even though the additional structure of string theory was a nuisance, the superstring had succeeded where other potentially more economical theories had failed.

Two further significant developments soon ensured string theory’s inclusion in the physics canon. One was from the Princeton collaboration of David Gross, Jeff Harvey, Emil Martinec, and Ryan Rohm, who in 1985 derived a theory that they named the
heterotic string
. This word is derived from the word “heterosis,” which in botany means “hybrid vigor,” a term used to refer to hybrid organisms with properties superior to those of their progenitors. In string theory, a vibrational mode can move either clockwise or counterclockwise along the string. The name “heterotic” was used because waves moving to the left were treated differently from those waves moving to the right, and consequently the theory included more interesting forces than did the versions of string theory that were already known.

The discovery of the heterotic string was further confirmation that
the forces that Green and Schwarz had discovered to be anomaly-free and acceptable in ten dimensions were truly special. They had found several sets of forces, including all of those that had already been shown to be possible in string theory, as well as another set of forces that had never before been discovered (theoretically) to be part of string theory. The forces of the heterotic string were precisely the new ones that Green and Schwarz had shown were free from anomalies. With the heterotic string, this additional set of forces, which could include those of the Standard Model, was shown not only to be a true string theory possibility, but one that could be realized explicitly. Physicists considered the heterotic string a real breakthrough in the attempt to relate string theory to the Standard Model.

There was one final development that cemented string theory’s prominence. This discovery dealt with the extra dimensions essential to the superstring. It is all well and good to show that superstring theory is internally consistent and embodies the forces of the Standard Model, but this is not very interesting if you are stuck with the wrong number of dimensions of space. Superstring theory stipulates ten dimensions. The world around us appears to contain only four (including time). Something needs to be done about the superfluous six.

Physicists now think that one answer might be compactification—rolled-up dimensions of an imperceptibly small size, as described in Chapter 2. At first, however, this curling up of extra dimensions didn’t seem the right way to treat the extra dimensions of string theory. The problem was that theories with rolled-up dimensions could not reproduce the important (and surprising) feature of the weak force discussed in Chapter 7: the weak force treats left-and right-handed particles differently. This is not a mere technical detail. The entire structure of the Standard Model relies on left-handed particles being the only ones that experience the weak force. Otherwise, few predictions of the Standard Model would work.

Although ten-dimensional string theory could treat left-and right-handed particles differently, it appeared that this would no longer be true once the six extra dimensions were rolled up. The resulting four-dimensional effective theory always contained neatly matched pairs of left-and right-handed particles. All of the forces that acted on left-handed fermions also acted on right-handed ones, and vice
versa. If string theory could not find a way out of this impasse, it would have to be scrapped.

In 1985, Philip Candelas, Gary Horowitz, Andy Strominger, and Edward Witten recognized the significance of a more subtle and complicated way to curl up the extra dimensions, namely a compactification known as
Calabi-Yau manifolds
. The details are complicated, but basically Calabi-Yau manifolds leave a four-dimensional theory that can distinguish left from right and potentially produce the particles and forces of the Standard Model, including the parity-violating weak force. Furthermore, rolling up the extra dimensions into a Calabi-Yau manifold preserves supersymmetry.
^*
With the Calabi-Yau breakthrough, superstring theory was in business.

In many physics departments, superstring theory superseded particle physics, and the superstring revolution was more like a coup. Because superstring theory incorporates quantum gravity and could contain the known particles and forces, many physicists went so far as to think of it as the ultimate theory that underlies everything. Indeed, in the 1980s string theory was dubbed the “Theory of Everything” (or “TOE”). String theory was more ambitious even than Grand Unified Theories: with string theory, physicists hoped to unify all forces (including gravity) at an energy higher even than the energy associated with GUTs. Even without any observations that supported string theory, many physicists decided that string theory’s potential for reconciling quantum mechanics and gravity was reason enough to support its claim to prominence.

The Endurance of the Old Regime

If string theorists are right, and the world is ultimately composed of fundamental oscillating strings, must all of particle physics then be abandoned? The answer is a resounding “No.” The goal of string
theory is to reconcile quantum mechanics and gravity at distances smaller than the Planck scale length, where we believe that a new theory takes over. Therefore, in conventional string theory (as opposed to the variants suggested by extra-dimensional models), a string should be about the Planck scale length in size. That tells us that in conventional string theory, the differences between particle physics and string theory should appear only at this tiny Planck scale length or, equivalently, at the ultra-high Planck scale energy, where gravity is expected to be strong. This size is so tiny, and this energy so high, that strings would in no way obviate the particle description at experimentally accessible energies.

For energies below the Planck scale energy a particle physics description is in fact quite adequate. If a string is so small that its length is undetectable, the string might as well be a particle; no experiment could tell the difference. Particles and Planck-length strings are indistinguishable. The string’s one-dimensional extent is just as invisible to us as the tiny curled-up extra dimensions we considered earlier. Unless we have instruments that can handle sizes of order 10
^-33
cm, such a string is much too small to see.

It makes sense that string theory and particle physics look the same at achievable energies. The uncertainty principle tells us that the only way to study small distances is with high-momentum particles, which are very energetic. Therefore, without sufficient energy, you have no way of seeing that the string is long and skinny, rather than pointlike.

In principle, we could find evidence to support string theory by searching for the many new particles it predicts—the particles that correspond to the many possible oscillations of the string. The problem with this strategy is that most new string-induced particles would be extremely heavy, with a mass as big as the Planck scale mass, 10
¹⁹
GeV. This mass is huge compared with the mass of particles that have been detected experimentally, the heaviest of which is about 200 GeV.

The extra particles that would arise from the oscillations of the string would be so heavy because the string’s
tension
—its resistance to stretching that determines how readily a string will oscillate and produce heavy particles—would be large. The Planck scale energy
determines the strings’ tension; this tension is required for string theory to reproduce the correct interaction strength for the graviton, and hence for gravity itself.
²⁵
The higher the string tension, the more energy is required to generate oscillations (just as it’s harder to pluck, or displace, a tight bowstring than a loose one). And this large energy translates into a large mass for the extra string-derived particles. These Planck-mass particles are too massive to be produced at any particle experiment operating today (or, most probably, in the future).

So, even if string theory is correct, we are unlikely to find the many additional heavy particles it predicts. The energy of current experiments is sixteen orders of magnitude too low. Because the extra particles are so extraordinarily heavy, the prospects for discovering evidence of strings experimentally is very poor, with the possible exception of the extra-dimensional models I’ll discuss later on.

In most string theory scenarios however, because the string length is so tiny and the string tension is so high, we won’t see any evidence to support string theory at the energies achievable in accelerators, even if the string description is correct. Particle physicists who are interested in predicting experimental results can safely apply conventional four-dimensional quantum field theory, ignore string theory, and still get the correct results. As long as you look only at sizes greater than 10
^-33
cm, (or, equivalently, energies below 10
¹⁹
GeV), nothing we have considered earlier about the low-energy consequences of particle physics would change. Given that the size of a proton is about 10
^-13
cm and that the maximum energy reach of current accelerators is about a thousand GeV, it’s a pretty safe bet that particle-theory predictions will suffice.

Even so, particle physicists who concentrate on low-energy phenomena have good reasons to pay attention to string theory. String theory introduces new ideas, both mathematical and physical, that no one would otherwise have considered, such as branes and other extra-dimensional notions. Even in four dimensions, string theory has paved the way to an improved understanding of supersymmetry, quantum field theory, and the forces a quantum field theory model might contain. And of course, if string theory does give a fully consistent quantum mechanical description of gravity, that would be
a formidable achievement. These benefits make string theory very worthwhile, even to those exclusively concerned with experimentally accessible phenomena. Although it will be very difficult (if not impossible) to detect strings, the theoretical ideas illuminated by string theory might be pertinent to our world. We’ll soon see what some of these might be.