More Arnold's N = 2 superconformal gauge theories

TL;DR

The article extends the 4d ${\cal N}=2$ wall-crossing/cluster-algebra framework to the quasi-homogeneous bimodal Arnold singularities, demonstrating that the resulting theories have finite BPS chambers and constructing their BPS spectra via quivers with potentials. It identifies two obstruction directions by modality, analyzes 2d wall-crossings and RG flows to justify physically realizable chambers, and computes flavor charges from the chiral ring data. A central result is the prediction of $11$ new periodic $Y$-systems arising from the associated quantum monodromies, providing evidence for a correspondence between thermodynamic Bethe ansatz periodic $Y$-systems and 4d ${\cal N}=2$ SCFTs with finite BPS chambers and chiral primaries of dimensions of the form $\mathbb{N}/\ell$. The work thus strengthens the link between geometric engineering, BPS quivers, and exactly solvable structures in low-dimensional theories, with implications for understanding non-Lagrangian corners and the web of dualities in ${\cal N}=2$ gauge theories.

Abstract

We study the N = 2 gauge theories obtained by engineering the Type IIB superstring on the quasi-homogeneous elements of Arnold's list of bimodal singularities. All these theories have finite BPS chambers and we describe, along the lines of [arXiv:1107.5747], the algebraically obvious ones. Our results leads to the prediction of 11 new periodic Y-systems, providing additional evidence for the correspondence in between thermodinamical Bethe ansatz periodic Y-systems and N = 2 superconformal theories with a finite BPS chamber whose chiral primaries have dimensions of the form $\mathbb{N}/\ell$.