BPS Structure of Argyres-Douglas Superconformal Theories

TL;DR

This paper investigates the geometric engineering of Argyres-Douglas superconformal theories via type IIB string theory on singular Calabi-Yau threefolds, focusing on counting BPS states through D3-brane degeneracies.

Contribution

It introduces a method to count BPS states in Argyres-Douglas theories by analyzing D3-branes on Calabi-Yau singularities, revealing finite degeneracies dependent on deformations.

Findings

Finite BPS state degeneracies depend on deformation parameters.

Degeneracy counts are analogous to kink solutions in 2D Landau-Ginzburg models.

Discussion of worldsheet theories near Calabi-Yau singularities.

Abstract

We study geometric engineering of Argyres-Douglas superconformal theories realized by type IIB strings propagating in singular Calabi-Yau threefolds. We use this construction to count the degeneracy of light BPS states under small perturbations away from the conformal point, by computing the degeneracy of D3-branes wrapped around supersymmetric 3-cycles in the Calabi-Yau. We find finitely many BPS states, the number of which depends on how this deformation is done, similarly to the degeneracy of kink solutions for the deformation of N=2 Landau-Ginzburg superconformal theories in two dimensions. Also, some aspects of worldsheet theories near general Calabi-Yau singularities are discussed.