A-D hypersurface of $su(n)$ $\mathcal{N}=2$ supersymmetric gauge theory with $N_f = 2n-2$ flavors

TL;DR

This paper derives conditions on moduli parameters that define the Argyres-Douglas hypersurface in a supersymmetric gauge theory, extending previous work on flavor mass relations and symmetry restoration in matrix models.

Contribution

It explicitly determines the moduli conditions for maximal degeneration of the Seiberg-Witten curve, characterizing the Argyres-Douglas hypersurface in the theory.

Findings

Derived concrete conditions on moduli parameters for maximal degeneration.

Identified the Argyres-Douglas hypersurface within the moduli space.

Extended previous flavor mass relation analysis to include curve degeneration.

Abstract

In the previous letter, arXiv:2210.16738[hep-th], we found a set of flavor mass relations as constraints that the $\beta$-deformed $A_{n-1}$ quiver matrix model restores the maximal symmetry in the massive scaling limit and reported the existence of Argyres-Douglas critical hypersurface. In this letter, we derive the concrete conditions on moduli parameters which maximally degenerates the Seiberg-Witten curve while maintaining the flavor mass relations. These conditions define the A-D hypersurface.