Power Towers of String Instantons for N=1 Vacua

We provide arguments for the existence of novel hereinafter called poly-instanton corrections to holomorphic couplings in four-dimensional N=1 supersymmetric string compactifications. After refining quantitatively the D-brane instanton calculus for corrections to the gauge kinetic function, we explicitly apply it to the Type I toroidal orbifold defined in arXiv:0710.3080 and compare the results to the proposed heterotic S-dual model. This leads us to the intriguing conclusion that N=1 string vacua feature a power tower like proliferation of instanton corrections.