We show by explicit construction the existence of various four dimensional models of type II superstrings with N=2 supersymmetry, purely vector multiplet spectrum and no hypermultiplets. Among these, two are of special interest, at the field theory level they correspond to the two exceptional N=2 supergravities of the magic square that have the same massless scalar field content as pure N=6 supergravity and N=3 supergravity coupled to three extra vector multiplets. The N=2 model of the magic square that is associated to N=6 supergravity is very peculiar since not only the scalar degrees of freedom but all the bosonic massless degrees of freedom are the same in both theories.
All presented hyper-free N=2 models are based on asymmetric orbifold constructions with N=(4,1) world-sheet superconformal symmetry and utilize the 2d fermionic construction techniques. The two exceptional N=2 models of the magic square are constructed via a "twisting mechanism" that eliminates the extra gravitini of the N=6 and N=3 extended supergravities and creates at the same time the extra spin-1/2 fermions and spin-1 gauge bosons which are necessary to balance the numbers of bosons and fermions. Theories of the magic square with the same amount of supersymmetry in three and five space-time dimensions are constructed as well, via stringy reduction and oxidation from the corresponding four-dimensional models.
