Star Shaped Quivers in Four Dimensions

We discuss 4D Lagrangian descriptions, across dimensions IR duals, of compactifications of the 6D (D, D) minimal conformal matter theory on a sphere with arbitrary number of punctures and a particular value of flux as a gauge theory with a simple gauge group. The Lagrangian has the form of a "star shaped quiver" with the rank of the central node depending on the 6D theory and the number and type of punctures. Using this Lagrangian one can construct across dimensions duals for arbitrary compactifications (any, genus, any number and type of USp punctures, and any flux) of the (D, D) minimal conformal matter gauging only symmetries which are manifest in the ultraviolet.