Trifectas for T N in 5d

The trinions TN are a class of 5d $$ \mathcal{N} $$ = 1 superconformal field theories (SCFTs) realized as M-theory on ℂ3/ℤN× ℤN . We apply to TN , as well as closely-related SCFTs that are obtained by mass deformations, a multitude of recently developed approaches to studying 5d SCFTs and their IR gauge theory descriptions. Thereby we provide a complete picture of the theories both on the Coulomb branch and Higgs branch, from various geometric points of view — toric and gluing of compact surfaces as well as combined fiber diagrams — to magnetic quivers and Hasse diagrams.