Prof Andre Lukas

Abstract:

We study machine learning of phenomenologically relevant properties of string compactifications, which arise in the context of heterotic line bundle models. Both supervised and unsupervised learning are considered. We find that, for a fixed compactification manifold, relatively small neural networks are capable of distinguishing consistent line bundle models with the correct gauge group and the correct chiral asymmetry from random models without these properties. The same distinction can also be achieved in the context of unsupervised learning, using an auto-encoder. Learning non-topological properties, specifically the number of Higgs multiplets, turns out to be more difficult, but is possible using sizeable networks and feature-enhanced data sets.

Abstract:

We identify a set of transforms on the Picard lattice of non-singular complex projective surfaces that map effective line bundles to nef line bundles, while preserving the dimension of the zeroth cohomology. These transforms can often be used in conjunction with vanishing theorems to compute the dimension of the zeroth cohomology in terms of a topological index. The method is illustrated on del Pezzo and Hirzebruch surfaces.