BPS spectrum of Argyres-Douglas theory via spectral network

TL;DR

This paper investigates the BPS spectrum of Argyres-Douglas theories derived from six-dimensional $(2,0)$ theories using spectral networks, revealing equivalences between theories of different ranks through wall-crossing analysis.

Contribution

It provides a systematic spectral network approach to analyze BPS spectra and demonstrates equivalences of $ =2$ superconformal theories from different six-dimensional origins.

Findings

Confirmed the chamber structure and wall-crossing phenomena in Argyres-Douglas theories.

Provided evidence for the equivalence of theories with different ranks.

Applied spectral networks to study BPS spectra in superconformal field theories.

Abstract

We study the BPS spectrum of four-dimensional $\mathcal{N}=2$ superconformal field theory of Argyres-Douglas type, obtained via twisted compactification of six-dimensional $A_{N-1}$ $(2,0)$ theory on a sphere with an irregular puncture, by using spectral networks. We give strong evidence of the equivalence of $\mathcal{N}=2$ superconformal field theories from six-dimensional theories of different ranks by systematically comparing the chamber structure and wall-crossing phenomena.