The Chiral Ring of $N=2$ in Eight Dimensions

We study the non-perturbative corrections generated by exotic instantons in U(N) gauge theories in eight and four dimensions. As it was shown previously, the eight-dimensional prepotential can be resummed using a plethystic formula showing only a dependence from the center of mass and from a U(1) gauge factor. On the contrary, chiral correlators in eight and four dimensions display a non-trivial dependence from the full gauge group. Furthermore the resolvent, the generating function for the eight and four dimensional correlators, can be written in a compact form both in the eight and four dimensional cases.