Learning BPS Spectra and the Gap Conjecture
This work addresses a specific problem in theoretical physics related to BPS spectra and gap conjectures, representing an incremental advancement in applying machine learning techniques to analyze supersymmetric theories.
The paper investigates gaps between exponents in BPS q-series for 3d N=2 supersymmetric theories, finding that gaps at the start of the series are statistically more significant than those at higher powers. This result is derived using principal component analysis to analyze feature saliencies in the q-series data.
We explore statistical properties of BPS q-series for 3d N=2 strongly coupled supersymmetric theories that correspond to a particular family of 3-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.