Learning BPS Spectra and the Gap Conjecture

TL;DR

This paper investigates the statistical properties of BPS q-series in 3d N=2 supersymmetric theories linked to specific 3-manifolds, revealing significant gap patterns at the series' start using machine learning analysis.

Contribution

It introduces a novel statistical analysis of BPS q-series, applying explainable machine learning to uncover gap significance patterns in the series.

Findings

Gaps are more significant at the beginning of the q-series.

Principal component analysis reveals feature saliencies related to gap patterns.

The study provides new insights into the structure of BPS spectra in supersymmetric theories.

Abstract

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.