BPS states in N = 3 superstrings Original Research Article

The N = 3 string models are special solutions of the type II perturbative string theories. We present explicit expressions for the helicity supertraces, which count the number of perturbative BPS multiplets. Assuming the non-perturbative duality (S ↔ T) of the heterotic string on T6 and type II on K3 × T2 valid in N = 4 theories, we derive the N = 3 non-perturbative BPS mass formula by “switching off” some of the N = 4 charges and “fixing” some of the N = 4 moduli to special values. This operation corresponds to a well-defined Z2 projection acting freely on the compactification manifold. The consistency of this projection and the precise connection of the N = 4 and N = 3 BPS spectrum is shown explicitly in several type II string constructions. The heterotic N = 3 and some asymmetric type II constructions turn out to be non-perturbative with the S moduli fixed at the self-dual point S = i. Some of the non-perturbative N = 3 type II are defined in the context of F-theory.