Exotic instanton counting and heterotic/type I′ duality

We compute the partition function for the exotic instanton system corresponding to D-instantons on D7 branes in Type I′ theory. We exploit the BRST structure of the moduli action and its deformation by RR background to fully localize the integration. The resulting prepotential describes non-perturbative corrections to the quartic couplings of the gauge field F living on the D7's. The results match perfectly those obtained in the dual heterotic theory from a protected 1-loop computation, thus providing a non-trivial test of the duality itself.