Heterotic strings in symmetric and asymmetric orbifold backgrounds

We present a general formalism for constructing four-dimensional string models from Z_N orbifolds. An explicit form for the generalized GSO projector in the construction of twisted and untwisted states is provided, allowing then the computation of the massless spectrum for any embedding of the point group in the gauge degrees of freedom. Constant background fields, in particular Wilson lines, are considered, and the general constraints on them are presented for both symmetric and asymmetric orbifolds. Several examples are provided, including a general classification of the Z₃ orbifold models with one Wilson line, a systematic search for SU(3) × SU(2) × U(1)ⁿ models with three generations, models with tontinuous symmetry breaking and lower rank, and asymmetric orbifold models with and without Wilson lines.