Orbifold compactifications of string theory

The compactification of the heterotic string theory on a six-dimensional or bifold is attractive theoretically since it permits the full determination of the emergent four-dimensional effective supergravity theory, including t he gauge group and matter content, the superpotential and Kahler potential, as well as the gauge kinetic function. This review attempts to survey all of these calculations, covering the construction of orbifolds which yield ( four-dimensional space-time) supersymmetry; orbifold model building, includ ing Wilson lines, and the modular symmetries associated with orbifold compa ctifications; the calculation of the Yukawa couplings, and their connection with quark and lepton masses and mixing; the calculation of the Kahler pot ential and its string loop threshold corrections; and the determination of the non-perturbative effective potential for the moduli arising from hidden sector gaugino condensation, and its connection with supersymmetry breakin g. We conclude with a brief discussion of the relevance of weakly coupled s tring theory in the light of recent developments on the strongly coupled th eory. (C) 1999 Elsevier Science B.V. All rights reserved.