Ebook: Orbifold compactifications of string theory

The compactification of the heterotic string theory on a six-dimensional orbifold is attractive theoretically, since it permits the full determination of the emergent four-dimensional effective supergravity theory, including the 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, including Wilson lines, and the modular symmetries associated with orbifold compactifications; the calculation of the Yukawa couplings, and their connection with quark and lepton masses and mixing; the calculation of the Kahler potential 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 breaking. We conclude with a brief discussion of the relevance of weakly coupled string theory in the light of recent developments on the strongly coupled theory.