Aspects of type I-type II-heterotic triality in four dimensions

We discuss the equivalence between type I, type II and heterotic N = 2 superstring theories in four dimensions. We study the effective field theory of type I models obtained by orientifold reductions of type IIB compactifications on K₃ × T². We show that the perturbative prepotential is determined by the one-loop corrections to the Planck mass and is associated to an index. As is the case for threshold corrections to gauge couplings, this renormalization is entirely due to N = 2 BPS states that originate from D = 6 massless string modes. We apply our result to the so-called S-T-U model which admits simultaneous type II and heterotic descriptions, and show that all three prepotentials agree in the appropriate limits as expected from the superstring triality conjecture.