Trifectas for TN in 5d

Abstract

The trinions T_N are a class of 5d $\mathcal{N}$ = 1 superconformal field theories (SCFTs) realized as M-theory on ℂ³/ℤ_N× ℤ_N . We apply to T_N , 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.