Spectra of heterotic strings on orbifolds

We obtain the spectrum of heterotic strings compactified on orbifolds, focusing on its algebraic structure. Affine Lie algebra provides its current algebra and representations. In particular, the twisted spectrum and the Abelian charge are understood. A twisted version of algebra is used in the homomorphism from the orbifold action to the group action. The relation between the conformal weight and the mass gives a useful rule.