The equivalence of NSR and GS four-dimensional twisted strings

Using a general construction of the modular invariant partition function for four-dimensional strings with twisted, orbifold-like, boundary conditions, we discuss the equivalence of their Neveu-Schwarz-Ramond and Green-Schwarz formulations. Four-dimensional GS strings are found to be equivalent to the class of NSR theories on orbifolds based on the canonical, free supercurrent, with underlying N=2 linear world-sheet supersymmetry. This equivalence provides interesting insights on the consistency conditions for all order modular invariance to be applied on four-dimensional Green-Schwarz strings. (orig.)