Maruyoshi-Song flows and defect groups of Dₚᵇ(G) theories

We study the defect groups of Dₚᵇ Dpb (G) theories using geometric engineering and BPS quivers. In the simple case whenb=h∨(G), we use the BPS quivers of the theory to see that the defect group is compatible with a known Maruyoshi-Song flow. To extend to the case whereb≠h∨(G), we use a similar Maruyoshi-Song flow to conjecture that the defect groups of Dₚᵇ Dpb (G) theories are given by those ofG(b)[k] theories. In the cases ofG=An,E6,E8we cross check our result by calculating the BPS quivers of theG(b)[k] theories and looking at the cokernel of their intersection matrix.