Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 052, 41 pages      arXiv:1511.01421      https://doi.org/10.3842/SIGMA.2019.052

BPS Spectra, Barcodes and Walls

Michele Cirafici abc
a) Department of Mathematics and Geoscience, Università di Trieste, and INFN, Sezione di Trieste, Via A. Valerio 12/1, I-34127 Trieste, Italy
b) CAMGSD, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
c) Institut des Hautes Études Scientifiques, Le Bois-Marie, 35 route de Chartres, F-91440 Bures-sur-Yvette, France

Received November 12, 2018, in final form July 04, 2019; Published online July 09, 2019

Abstract
BPS spectra give important insights into the non-perturbative regimes of supersymmetric theories. Often from the study of BPS states one can infer properties of the geometrical or algebraic structures underlying such theories. In this paper we approach this problem from the perspective of persistent homology. Persistent homology is at the base of topological data analysis, which aims at extracting topological features out of a set of points. We use these techniques to investigate the topological properties which characterize the spectra of several supersymmetric models in field and string theory. We discuss how such features change upon crossing walls of marginal stability in a few examples. Then we look at the topological properties of the distributions of BPS invariants in string compactifications on compact threefolds, used to engineer black hole microstates. Finally we discuss the interplay between persistent homology and modularity by considering certain number theoretical functions used to count dyons in string compactifications and by studying equivariant elliptic genera in the context of the Mathieu moonshine.

Key words: string theory; supersymmetry; BPS states; persistent homology.

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