Novel wall-crossing behaviour in rank one $\mathcal{N}=2^*$ gauge theory

TL;DR

This paper investigates the complex BPS spectrum of a specific $ ext{SU}(2)$ $ ext{N}=2^*$ gauge theory, revealing novel wall-crossing phenomena involving interactions between BPS particles with negative pairings.

Contribution

It uncovers unexpected wall-crossing behaviors in the BPS spectrum of $ ext{SU}(2)$ $ ext{N}=2^*$ gauge theory, expanding understanding of spectrum interactions and orderings.

Findings

Discovery of wall-crossings involving negative electric-magnetic pairings.

Identification of new states in the BPS spectrum.

Interpretation of reverse orderings in wall-crossing formulas.

Abstract

We study the BPS spectrum of four-dimensional $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge group $SU(2)$ and a massive adjoint hypermultiplet, which has an extremely intricate structure with infinite spectrum in all chambers of its Coulomb moduli space, and is not well understood. We build on previous results by employing the BPS quiver description of the spectrum, and explore the qualitative features in detail using numerical techniques. We find novel and unexpected behaviour in the form of wall-crossings involving interactions between BPS particles with negative electric-magnetic pairings, which we interpret in terms of the reverse orderings of the usual wall-crossing formulas for rank one $\mathcal{N}=2$ field theories. This identifies new a priori unrelated states in the spectrum.