BPS Structure of Argyres–Douglas Superconformal Theories

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 supersym-metric 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 .