Eluding SUSY at every genus on stable closed string vacua

In closed string vacua, ergodicity of unipotent ows provide a key for relat-ing vacuum stability to the UV behavior of spectra and interactions. Infrared finiteness at all genera in perturbation theory can be rephrased in terms of cancelations involving only tree-level closed strings scattering amplitudes. This provides quantitative results on the allowed deviations from supersymmetry on perturbative stable vacua. From a math-ematical perspective, diagrammatic relations involving closed string amplitudes suggest a relevance of unipotent ows dynamics for the Schottky problem and for the construction of the superstring measure. © SISSA 2011.