Aspects of the string theory compactified on orbifold

Abstract

The orbifold compactification of superstring theories, especially the heterotic string theory, is reviewed. After providing some general properties of orbifolds, we discuss the orbifolds made out of tori and also the various constraints on orbifold compactification. The most crucial one is the existence of twisted sectors and the need is shown with an example, the conformal field theory of $S^1/Z_2$ on a torus. In addition, the compactification of the heterotic string theory on a $Z_3$ orbifold is discussed in detail. The massless spectrum and the low energy effective action are obtained. Some aspects of the effective action regarding the supersymmetry breaking are also discussed.