Topological Data Analysis for the String Landscape

Understand

Persistent homology computes the multiscale topology of a data set by using a sequence of discrete complexes.

• In this paper, we propose that persistent homology may be a useful tool for studying the structure of the landscape of string vacua.
• As a scaled-down version of the program, we use persistent homology to characterize distributions of Type IIB flux vacua on moduli space for three examples: the rigid Calabi-Yau, a hypersurface in weighted projective space, and the symmetric six-torus $T^6=(T^2)^3$.
• These examples suggest that persistence pairing and multiparameter persistence contain useful information for characterization of the landscape in addition to the usual information contained in standard persistent homology.