Title:

Machine Learning in the String Landscape

Modern formulations of string theory require a spacetime structure that is at least (9+1)-dimensional. For these theories to be phenomenologically relevant, six of nine spactial dimensions must be ``compactified'' to agree with experimental evidence of a (3+1)-dimensional spacetime structure. These compactified dimensions take the form of a Calabi-Yau manifold of complex dimension 3 (Calbi-Yau 3-fold). The number of choices for compactification has a lower bound of around $10^{500}$, thus the idenification of Calabi-Yau 3-folds by way of machine learning can be an important tool for research. We first identify each Calabi-Yau n-fold to a particular reflexive polytope in an (n+1)-dimensional complex projective space. The vertex coordinates for each polytope contain all the information needed to reconstruct the Calabi-Yau n-fold. These are used as the source of data for a fully-connected neural network model to learn from and identify groups of polytopes based on certain topological properties of the related manifolds. As a test case, the model is first given data for the 16 reflexive 2-dimensional polytopes as well as many different configurations of these polytopes to increase the total amount of sample data. With the 2-dimensional polytopes the model achieved at most an accuracy of 97.32\%. The 4319 reflexive 3-dimensional polytopes are analyzed next and we are able to identify the correct polytope group at most 86.9\% of the time with current models. We hope to address the possibly phenomenologically relevant case of the 4-dimensional polytopes in the future.

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