5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities

TL;DR

This paper explores the geometric origins of 4d and 5d superconformal field theories from string theory singularities, introduces new trinions, and uncovers novel S-dualities through quiver analysis.

Contribution

It introduces a class of trinion singularities leading to new 4d SCFTs, analyzes their 3d reductions, and discovers new S-dualities and methods to handle magnetic quiver badness.

Findings

Identification of $D_p^b(G)$-trinions as marginal gaugings of SCFTs.

Development of a framework to resolve magnetic quiver badness using class $ ext{S}$ realization.

Discovery of new S-dualities, including an $E_8$ gauging dual to an $E_8$-shaped Lagrangian quiver.

Abstract

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 $\mathcal{N}=2$ SCFTs that we call $D_p^b(G)$-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 $\mathcal{N}=4$ 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 $\mathcal{S}$ realization. We also discover new S-dualities between different $D_p^b(G)$-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.