Four Years In The Making: A Superstring Revolution

In August 1984, M. Green and J. Schwarz ushered in the latest revolution in particle physics with their discovery of mathematically consistent superstring theories. Since then, there has been a vast effort to understand string theory and to bring it to bear on the major unsolved problems of particle physics. Some have hailed it as the final unified theory of everything, while others have damned it as recreational mathematics, theology, or something worse. What is the theory that has caused this controversy and what is at the root of the turmoil? The basic idea of string theory is to replace elementary particles such as photons, electrons, quarks, and gravitons with open or closed loops of string. These strings are supposed to be the fundamental stuff of which all matter and all forces are made. They can carry charges, either stuck on the ends of open strings, or flowing as currents along closed strings. The different vibrational modes of the string correspond to different “elementary particles,” and the interactions between particles correspond to breaking and joining bits of string. Amazingly, this unlikely picture has been enormously successful at duplicating the known particle species and the interactions between them. All known particles can be realized as different modes of the string, and the interactions between them dictated by the consistency of string theory are just the types of interactions that appear in the current standard model of particle physics. In addition, the problems associated with infinite quantities that plagued most theories of particles (particularly quantized theories of gravity) are removed in string theory. Experience has taught us that as we probe shorter distances and higher energies, the laws of physics become at the same time simpler and more tightly constrained by mathematical consistency. This tendency reaches its peak in string theory where the possible types of theories are limited to a very small number (six at present) and even the number of space-time dimensions is fixed by the internal consistency of the theory. String theory, if it is correct, is truly a theory of everything. It contains no adjustable parameters and must either describe the real world or be rejected. In this respect it is vastly superior to the standard model of particle physics, which contains a plethora of parameters that are not fixed by the internal dynamics or consistency of the theory, but must be determined by experiments. There is, of course, a high price to be paid for these wonders. String theory requires nine spatial dimensions, so one has to assume that six of them are so small that they have so far escaped notice. The modifications of ordinary particle physics due to string physics only occur at energies that are inaccessible to any foreseeable accelerator, making experimental tests of string theory extremely difficult. And finally, the mathematics needed to explore string theory is more advanced than most particle physicists are used to, and in some cases is on the leading edge of current mathematical research. Current research in string theory can be divided into three broad areas: the study of the “internal” six spatial dimensions and their effect on the masses and interactions of the lightest modes of the string, which are supposed to comprise the observed particles; the development of techniques for calculating how strings scatter and the search for a fundamental formulation of string theory. The “compactification” of the six internal dimensions turns out to be linked with the apparently unrelated problem of critical phenomena in two dimensions. the connection arises because the propagation of strings in space is essentially a two-dimensional problem—one dimension for the spatial coordinate of the string the other for the time that labels configuration of the string. This propagation must also preserve a set of symmetries, including the symmetry of scale transformations. These symmetries are precisely those known to characterize phase transitions in two-dimensional systems. As a result, string theorists, mathematical physicists, and statistical mechanicians are collaborating to classify the possible phase transitions in two dimensions and thereby the possible types of string “compactification.” This problem also appears to be connected in poorly understood ways to problems as diverse as the classification of finite groups and the structure of knot invariants. Present techniques in string theory allow one to calculate the scattering of strings according to the number of times they split and rejoin. As the number of splittings grows, the calculations involve complicated sums in dealing with intermediate configurations, which occur after the strings join and before they part. There has been a great deal of progress in the last few years in understanding how to set up these calculations in a way that reveals the symmetries of the problem. One of the string theorists’ goals is to be able to show that one obtains finite answers to these calculations. Recent results have put string theorists close to attaining this goal. The outstanding problem of string theory is to understand its full structure. We now understand a small piece of the theory that governs the splitting and joining of strings. But we suspect there is a more fundamental formulation that should allow us to define the theory independently of this splitting and rejoining. It would also reveal the hidden symmetries or structures that give string theory its marvelous properties. Most work in this direction has been devoted to extending the ideas of the field theory to string theory. However, progress in this direction has been slow and many workers are now searching for some other way of formulating string theory that does not rely as heavily on analogies with the theories of point particles. The last four years have dampened hopes that string theory will soon lead to a detailed understanding of quantum gravity and the structure of the standard model. But unlike many previous attempts at unified theories, string theory has not been shown to contain any internal inconsistencies or flaws that would rule it out as the correct theory. Instead, it has turned out that our understanding of the theory is still at too primitive a stage to allow any kind of detailed calculation of testable quantities. Because of this, and because string theorists are forced to proceed without any experimental guidance, some physicists have tried to argue that string theory is not physics at all and should be abandoned before it corrupts a whole generation of particle physicists. Supporters of string theory in return point to examples of theories that underwent many years of theoretical development before leading to any testable prediction. A classic example is provided by the gauge theories that underlie the standard model of particle physics. The comparison is not a perfect one, however. Usually, only a small part of the particle physics community has pursued such far-out theoretical ideas, whereas string theory is now being pursued by a substantial part of the community. Why have so many gone so far out on a limb? The answer lies in the combination of the success of particle theorists in developing the standard model and the increasing difficulty and expense of high-energy experiments. One conservative response to this situation is for theorists to consolidate understanding of the standard model while waiting for new experimental results. There is much work yet to be done on quantum chromodynamics (QCD), the theory of strong interactions. A quantitative understanding of confinement of quarks is still lacking. QOD is also playing an increasingly important role in our understand ing of nuclear physics. And our understanding of the weak interactions is also far from perfect: The main mystery has to do with the mechanism that breaks the symmetry between electromagnetic and weak interactions. Here the theorists seem to have run out of steam. Several mechanisms have been proposed with experimentally testable predictions. It is now up to the experimentalists to decide which mechanism, if any, is correct. Beauty, Depth, Elegance On the other band, the goal of particle physics has always been to push our understanding of the fundamental structure of the world to the farthest possible limits. String theory represents a quantum jump in our ability to contemplate questions that were previously beyond our ken. It is a theory of great beauty, depth, and elegance. One can argue that the particle physics community needs a better balance between the conservative approach and the alternative of string theory. To suggest, however, as some have done, that string theory is not physics, or that string theorists should not be employed and allowed to “pervert” graduate students smacks of intellectual cowardice. Pursuits such as string theory are crucial to the long term health of the field and should be allowed to live or die on their own merits. Jeffrey A. Harvey is an associate professor of physics at Princeton University, Princeton, N.J. The Princeton “string quartet” includes Harvey, D.J. Gross, E. Martinec, and R. Rohm.

Four Years In The Making: A Superstring Revolution

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