are predicting the End of Science on the grounds that all the important discoveries have already been made, it is worth emphasizing that the two main pillars of 20th-century physics, quantum mechanics and Einstein’s general theory of relativity, are mutually incompatible. General relativity fails to comply with the quantum rules that govern the behavior of elementary particles, whereas on the opposite scale, black holes are challenging the very foundations of quantum mechanics. Something big has to give. This predicament augurs less the bleak future of diminishing returns predicted by the millennial Jeremiahs and more another scientific revolution. Until recently, the best hope for a theory that would unite gravity with quantum mechanics and describe all physical phenomena was based on strings: one-dimensional objects whose modes of vibration represent the elementary particles. In the past two years, however, strings have been subsumed by M-theory. In the words of the guru of string theory (and according to Life magazine, the sixth most influential American baby boomer), Edward Witten of the Institute for Advanced Study in Princeton, N.J., “M stands for Magic, Mystery or Membrane, according to taste.” New evidence in favor of this theory is appearing daily, representing the most exciting development since strings first swept onto the scene. M-theory, like string theory, relies crucially on the idea of supersymmetry. Physicists divide particles into two classes, according to their inherent angular momentum, or “spin.” Supersymmetry requires that for each known particle having integer spin—0, 1, 2 and so on, measured in quantum units—there is a particle with the same mass but half-integer spin (1/2, 3/2, 5/2 and so on), and vice versa. Unfortunately, no such superpartner has yet been found. The symmetry, if it exists at all, must be broken, so that the postulated particles do not have the same mass as known ones but instead are too heavy to be seen in current accelerators. Even so, theorists have retained belief in supersymmetry primarily because it provides a framework within which the weak, electromagnetic and strong forces may be united with the most elusive force of all: gravity. Supersymmetry transforms the coordinates of space and time such that the laws of physics are the same for all observers. Einstein’s general theory of relativity derives from this condition, and so supersymmetry implies gravity. In fact, supersymmetry predicts “supergravity,” in which a particle with a spin of 2—the graviton—transmits gravitational interactions and has as a partner a gravitino, with a spin of 3/2. Conventional gravity does not place any limits on the possible dimensions of space-time: its equations can, in principle, be formulated in any dimension. Not so with supergravity, which places an upper limit of 11 on the dimensions of space-time. The familiar universe, of course, has three dimensions of space: height, length and breadth, while time makes up the fourth dimension of spacetime. But in the early 1920s Polish physicist Theodore Kaluza and Swedish physicist Oskar Klein suggested that spacetime may have a hidden fifth dimension. This extra dimension would not be infinite, like the others; instead it would close in on itself, forming a circle. Around that circle could reside quantum waves, fitting neatly into a loop. Only integer numbers of waves can fit around the circle; each of these would corre-

We review the status of solitons in superstring theory, with a view to understanding the strong coupling regime. These solitonic solutions are non-singular field configurations which solve the empty-space low-energy field equations (generalized, whenever possible, to all orders in α′), carry a non-vanishing topological “magnetic” charge and are stabilized by a topological conservation law. They are compared and contrasted with the elementary solutions which are singular solutions of the field equations with a σ-model source term and carry a non-vanishing Noether “electric” charge. In both cases, the solutions of most interest are those which preserve half the space-time supersymmetries and saturate a Bogomol'nyi bound. They typically arise as the extreme mass = charge limit of more general two-parameter solutions with event horizons. We also describe the theory dual to the fundamental string for which the roles of elementary and soliton solutions are interchanged. In 10 space-time dimensions, this dual theory is a superfivebrane and this gives rise to a string/fivebrane duality conjecture according to which the fivebrane may be regarded as fundamental in its own right, with the strongly coupled string corresponding to the weakly coupled fivebrane and vice versa. After compactification to four space-time dimensions, the fivebrane appears as a magnetic monopole or a dual string according as it wraps around five or four of the compactified dimensions. This gives rise to a four-dimensional string/string duality conjecture which subsumes a Montonen-Olive type duality in that the magnetic monopoles of the fundamental string correspond to the electric winding states of the dual string. This leads to a duality of dualities whereby under string/string duality the strong/weak coupling S-duality trades places with the minimum/maximum length T-duality. Since these magnetic monopoles are extreme black holes, a prediction of S-duality is that the corresponding electric massive states of the fundamental string are also extreme black holes. This is indeed the case.

A recently proposed method for evaluating effective Lagrangians is applied to the Yang--Mills field. (AIP)

We give an elementary introduction to the theory of supermembranes.