From Quivers to Geometry: 5d Conformal Matter

We show that all 5d balanced (ADE-shaped) special unitary quivers with no Chern-Simons level admit a UV completion which is a 5d conformal matter SCFT. We give explicit local Calabi-Yau threefolds realizing each of these models in M-theory. This unified description enables a systematic exploration of their physical properties, such as their Higgs Branch, as well as connections to class-S constructions and the affine Grassmannian.