Prof Andre Lukas

Abstract:

The immensity of the string landscape and the difficulty of identifying solutions that match the observed features of particle physics have raised serious questions about the predictive power of string theory. Modern methods of optimisation and search can, however, significantly improve the prospects of constructing the standard model in string theory. In this paper we scrutinise a corner of the heterotic string landscape consisting of compactifications on Calabi-Yau three-folds with monad bundles and show that genetic algorithms can be successfully used to generate anomaly-free supersymmetric (Formula presented.) GUTs with three families of fermions that have the right ingredients to accommodate the standard model. We compare this method with reinforcement learning and find that the two methods have similar efficacy but somewhat complementary characteristics.

Abstract:

We present a detailed study of the effective cones of Calabi-Yau threefolds with h1,1 = 2, including the possible types of walls bounding the Kähler cone and a classification of the intersection forms arising in the geometrical phases. For all three normal forms in the classification we explicitly solve the geodesic equation and use this to study the evolution near Kähler cone walls and across flop transitions in the context of M-theory compactifications. In the case where the geometric regime ends at a wall beyond which the effective cone continues, the geodesics “crash” into the wall, signaling a breakdown of the M-theory supergravity approximation. For illustration, we characterise the structure of the extended Kähler and effective cones of all h1,1 = 2 threefolds from the CICY and Kreuzer-Skarke lists, providing a rich set of examples for studying topology change in string theory. These examples show that all three cases of intersection form are realised and suggest that isomorphic flops and infinite flop sequences are common phenomena.

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 autoencoder. Learning nontopological properties, specifically the number of Higgs multiplets, turns out to be more difficult, but is possible using sizeable networks and feature-enhanced datasets.