Research and Instruction in String Theory

Abstract

Obtaining a unified description of all of the fundamental forces of nature is an old dream of theoretical physicists. At the present time, superstring theory is the only consistent quantum-mechanical model for describing particles with gravitational and Yang-Mills interactions. All other attempts to unify these forces suffer from quantum-mechanical divergences in scattering amplitudes that cannot be removed by renormalization. Even if superstring theory is not the final theory of unification, it probably contains some essential ingredients of such a theory.Although superstring theory exists since 1972, until recently, the only available method for studying superstrings used perturbative techniques. These techniques were useful for studying scattering amplitudes of gravitons, but were useless for studying non-perturbative gravitational phenomena such as black boles. However, in 1994, a symmetry of superstring theory was discovered which relates the theory at strong and weak coupling. This symmetry was called S-duality, and is similar to the Montonen-Olive duality symmetry that relates super-Yang-Mills theory at strong and weak coupling. One ingredient of superstrings that is crucial for the absence of divergences and the existence of S-duality is spacetime supersymmetry. Nevertheless, in the usual Ramond-Neveu-Schwarz (RNS) formalism for the superstring, the effects of spacetime supersymmetry are extremely difficult to analyze. Although there exists an alternative Green-Schwarz (GS) formalism for the superstring where spacetime supersymmetry is manifest, the Green-Schwarz formalism can only be quantized in light-cone gauge which greatly reduces its usefulness. During the last ten years, my research has concentrated on understanding the roleof spacetime supersymmetry in the superstring. This research led rae to discover a new formalism for the superstring where spacetime supersymmetry is manifest and which can be quantized in covariant gauges. Because ít does not suffer from the problems of the RNS and GS formalisms, this new formalism is useful for studying the absence of divergences and the S-duality symmetry of the superstring... (AU)