Maruyoshi-Song flows and defect groups of $$ {\mathrm{D}}_{\mathrm{p}}^{\mathrm{b}} $$(G) theories
Saghar S. Hosseini, Robert Moscrop
Abstract
A bstract We study the defect groups of $$ {D}_p^b $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>D</mml:mi><mml:mi>p</mml:mi><mml:mi>b</mml:mi></mml:msubsup></mml:math> ( G ) theories using geometric engineering and BPS quivers. In the simple case when b = 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 where b ≠ h ∨ ( G ), we use a similar Maruyoshi-Song flow to conjecture that the defect groups of $$ {D}_p^b $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>D</mml:mi><mml:mi>p</mml:mi><mml:mi>b</mml:mi></mml:msubsup></mml:math> ( G ) theories are given by those of G ( b ) [ k ] theories. In the cases of G = A n , E 6 , E 8 we cross check our result by calculating the BPS quivers of the G ( b ) [ k ] theories and looking at the cokernel of their intersection matrix.