Heterotic SO(32) model building in four dimensions

Four dimensional heterotic SO(32) orbifold models are classified systematically with model building applications in mind. We obtain all ℤ₃, ℤ₇ and ℤ_2N models based on vectorial gauge shifts. The resulting gauge groups are reminiscent of those of type-I model building, as they always take the form SO(2n₀) × U(n₁) × ⋯ ×...×U(n_N-1) × SO(2n_N). The complete twisted spectrum is determined simultaneously for all orbifold models in a parametric way depending on n₀,⋯, n_N, rather than on a model by model basis. This reveals interesting patterns in the twisted states: They are always built out of vectors and anti-symmetric tensors of the U(n) groups, and either vectors or spinors of the SO(2n) groups. Our results may shed additional light on the 5-duality between heterotic and type-I strings in four dimensions. As a spin-off we obtain an SO(10) GUT model with four generations from the ℤ₄ orbifold.