Table of contents

This review is an elementary introduction to supersymmetry. The example of supersymmetric quantum mechanics is used to discuss the basic concepts of supersymmetry and its characteristic features: anticommuting variables, supercharges, the cancellation of divergences, the vanishing of the vacuum energy, the degeneracy of energy spectra, and the spontaneous breaking of supersymmetry. The form taken by supersymmetry in problems in quantum mechanics and nuclear physics is discussed. The use of a supersymmetric formalism in statistical physics and field theory is also discussed.

A review of elementary-particle models based on low-energy supersymmetry is given. Supersymmetry is used in these models to compensate the quadratic divergence in the radiative correction to the mass of the Higgs boson in the Weinberg-Salam model and to solve the hierarchy problem in grand unification theories. The standard low-energy SU(3) SU(2)_L U(1) theory is replaced in this approach with the supersymmetric theory. A large number of new particles with masses M_w is predicted. The properties of these particles and possible experimental searches for them are discussed. Models based on different ways of supersymmetry breaking are considered. The central place is given to models with supersymmetry breaking due to supergravity, which have been particularly actively discussed in the last two years. Proton decay in supersymmetric GUT models is analyzed. Introductory ideas on supersymmetry, necessary for the understanding of most of this review, are presented in Section 1 and in the Appendix.

Progress in the search for a unified theory of elementary particles is reviewed. The supersymmetrical Kaluza-Klein theories are described: 11-, 10-, and 6-dimensional models of supergravity. The methods of spontaneous compactification, with whose help the four-dimensional theories are obtained, are described. The properties of the massless sector—zero modes in the Kaluza-Klein theories—and the question of the stability of vacuum solutions are discussed. An important criterion for the selection of a self-consistent theory is the absence of anomalies. The basic formulas for multidimensional chiral and gravitational anomalies are presented. The mechanism of the cancellation of the anomaly for Green and Schwarz's 10-dimensional effective field theory of superstrings with the gauge groups SO(32) and E₈ × E₈ is described. The basic concepts and the results of the theory of superstrings are presented. This theory has no divergences and is at the present time a very attractive candidate for a unified theory of elementary particles.

The present review is a revised version of lectures given at the Bakuriani (Georgia) Workshop on High Energy Physics (January 1985). A discussion is given of the recently discovered phenomenon of instanton-generated dynamical symmetry breaking in supersymmetric gauge theories with matter. For a definite choice of the matter multiplets, the gauge invariance is necessarily spontaneously broken, the gauge bosons acquire mass, the variation of the coupling constant ceases, and a weak-coupling regime sets in. This sometimes also involves spontaneous breakdown of the supersymmetry. A description is given of the fundamental aspects as well as the specific dynamical scenarios realized in the most typical models.