Topological data analysis for the string landscape

Cole, Alex (0000 0001 0701 8607, Department of Physics, University of Wisconsin, Madison, WI, 53706, U.S.A.) ; Shiu, Gary (0000 0001 0701 8607, Department of Physics, University of Wisconsin, Madison, WI, 53706, U.S.A.)

14 March 2019

Abstract: 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. We also study how restricting to special vacua with phenomenologically interesting low-energy properties affects the topology of a distribution.


Published in: JHEP 1903 (2019) 054
Published by: Springer/SISSA
DOI: 10.1007/JHEP03(2019)054
arXiv: 1812.06960
License: CC-BY-4.0



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