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) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain residual terminal singularities and/or 3-cycles. We focus on a certain class of 'trinion' singularities which exhibit these properties. In Type IIB, they give rise to 4d N = 2 SCFTs that we call Dpb(G)-trinions, which are marginal gaugings of three SCFTs with G flavor symmetry. In order to understand the 5d physics of these trinion singularities in M-theory, we reduce these 4d and 5d SCFTs to 3d N = 4 theories, thus determining the electric and magnetic quivers (or, more generally, quiverines). In M-theory, residual terminal singularities give rise to free sectors of massless hypermultiplets, which often are discretely gauged. These free sectors appear as 'ugly' components of the magnetic quiver of the 5d SCFT. The 3-cycles in the crepant resolution also give rise to free hypermultiplets, but their physics is more subtle, and their presence renders the magnetic quiver 'bad'. We propose a way to redeem the badness of these quivers using a class S realization. We also discover new S-dualities between different Dpb(G)-trinions. For instance, a certain E-8 gauging of the E-8 Minahan-Nemeschansky theory is S-dual to an E-8-shaped Lagrangian quiver SCFT.

Automated summary

Canonical hypersurface singularities in M-theory and Type IIB string theory lead to 5d and 4d superconformal field theories (SCFTs), respectively. This paper focuses on a specific class of 'trinion' singularities in Type IIB, which give rise to 4d N = 2 SCFTs known as Dpb(G)-trinions. Reducing these 4d and 5d SCFTs to 3d N = 4 theories helps determine their electric and magnetic quivers.