BPS spectrum of Argyres-Douglas theory via spectral network

TL;DR

This work analyzes the BPS spectra of Argyres-Douglas type 4d ${ N}=2$ SCFTs obtained from twisted compactifications of 6d ${A}_{N-1}$(2,0) theory on spheres with irregular punctures, using spectral networks to access nonperturbative data across the Coulomb branch. By constructing ${\mathcal S}$-walls, joints, and their wall-crossings, the authors extract minimal and maximal BPS spectra for a wide range of ${A}_{n}$- and ${D}_{n}$-class theories and show precise equivalences between rank-different realizations (for example ${\rm S}[A_{1};{\nabla}_{n+5}]$ and ${\rm S}[A_{N-1};{\nabla}_{\rm I}]$). The key finding is that chamber structure, BPS content, and symmetry enhancements align across these dual descriptions, providing strong evidence for equivalences of ${\mathcal N}=2$ SCFTs arising from distinct 6d ranks. The results illustrate the power of spectral networks to map nonperturbative spectra and wall-crossing in AD-type theories, with implications for dualities and flavor-symmetry enhancements in the IR.

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.

Figures (66)

• Figure 1: 4d SCFTs from 6d $A_1$ theory.
• Figure 2: 4d SCFTs from 6d $A_{N-1}$ theory.
• Figure 3: ${\mathcal{S}}$-walls around a branch point. ${\mathcal{S}}_{jk}$-walls are denoted by solid lines with $(jk)$. The broken line denotes the branch cut.
• Figure 4: A Seiberg-Witten curve and ${\mathcal{S}}$-walls around a branch point of index 2
• Figure 5: ${\mathcal{S}}$-walls around an $\mathrm{SU}(2)$ puncture