Machine learning BPS spectra and the gap conjecture

Abstract

We explore statistical properties of Bogomol’nyi-Prasad-Sommerfield q-series for 3d N=2 strongly coupled supersymmetric theories that correspond to a particular family of three-manifolds Y. We discover that gaps between exponents in the q-series are statistically more significant at the beginning of the q-series compared to gaps that appear in higher powers of q. Our observations are obtained by calculating saliencies of q-series features used as input data for principal component analysis, which is a standard example of an explainable machine learning technique that allows for a direct calculation and a better analysis of feature saliencies. Published by the American Physical Society 2024