Twisted superstrings in four dimensions

We study the formulation of string theories in four dimensions with explicit space-time supersymmetry, allowing the string coordinates to have both shifted and twisted, orbifold-like, boundary conditions. The theories we construct are automatically tachyon-free and can have gauge groups of small ranks. As an example, we recover the Z3 orbifold model. We describe the construction of superstring theories with rank eight gauge groups, illustrated by an SO(10) x SU(3) x U(1) model. (orig.)