Argyres-Douglas Loci, Singularity Structures and Wall-Crossings in Pure N=2 Gauge Theories with Classical Gauge Groups

TL;DR

This paper explores the structure of singularities and wall-crossing phenomena in N=2 gauge theories with classical groups, proposing new methods to locate Argyres-Douglas points and analyzing BPS spectra.

Contribution

It introduces novel techniques to identify Argyres-Douglas loci in moduli space and computes dyon charges for pure SU(r+1) and Sp(2r) theories, linking singularities to wall-crossing.

Findings

Identified new methods to locate Argyres-Douglas points.

Computed dyon charges for massless states in specific gauge theories.

Connected singularity structures to wall-crossing phenomena.

Abstract

N=2 Seiberg-Witten theories allow an interesting interplay between the Argyres-Douglas loci, singularity structures and wall-crossing formulae. In this paper we investigate this connection by first studying the singularity structures of hyper-elliptic Seiberg-Witten curves for pure N=2 gauge theories with SU(r+1) and Sp(2r) gauge groups, and propose new methods to locate the Argyres-Douglas loci in the moduli space, where multiple mutually non-local BPS states become massless. In a region of the moduli space, we compute dyon charges for all 2r+2 and 2r+1 massless dyons for SU(r+1) and Sp(2r) gauge groups respectively for rank r>1. From here we elucidate the connection to the wall-crossing phenomena for pure Sp(4) Seiberg-Witten theory near the Argyres-Douglas loci, despite our emphasis being only at the massless sector of the BPS spectra. We also present 2r-1 candidates for the maximal Argyres-Douglas points for pure SO(2r+1) Seiberg-Witten theory.