5d and 4d SCFTs: canonical singularities, trinions and S-dualities

Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) 5d 4d, respectively. In this paper, we study canonical hypersurface whose resolutions contain residual terminal and/or 3-cycles. We focus on a certain class of `trinion' which exhibit these properties. IIB, they 4d $\mathcal{N}=2$ SCFTs that call $D_p^b(G)$-trinions, are marginal gaugings three with $G$ flavor symmetry. order understand the physics trinion M-theory, reduce 3d $\mathcal{N}=4$ theories, thus determining electric magnetic quivers (or, more generally, quiverines). free sectors massless hypermultiplets, often discretely gauged. These appear as `ugly' components quiver SCFT. The 3-cycles crepant resolution also but their is subtle, presence renders `bad'. propose way redeem badness using $\mathcal{S}$ realization. discover new S-dualities between different $D_p^b(G)$-trinions. For instance, $E_8$ gauging Minahan-Nemeschansky S-dual an $E_8$-shaped Lagrangian