New example of infinite family of quiver gauge theories

We construct a new infinite family of quiver gauge theories which blow down to the Xp,q quiver gauge theories found by Hanany, Kazakopoulos and Wecht. This family includes a quiver gauge theory for the third del Pezzo surface. We show, using Z-minimization, that these theories generically have irrational R-charges. The AdS/CFT correspondence implies that the dual geometries are irregular toric Sasaki-Einstein manifolds, although we do not know the explicit metrics