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Persistent homology and string vacua. (English) Zbl 1388.81505
Summary: We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by identifying which homological characteristics persist over a long range of scales. We apply these techniques in several contexts. We analyze $$\mathcal{N}=2$$ vacua by focusing on certain distributions of Calabi-Yau varieties and Landau-Ginzburg models. We then turn to flux compactifications and discuss how we can use topological data analysis to extract physical information. Finally we apply these techniques to certain phenomenologically realistic heterotic models. We discuss the possibility of characterizing string vacua using the topological properties of their distributions.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
javaPlex; jHoles
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