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

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.

95 pages; v2: added references and corrected typos; v3&v4: added references and footnotes, JHEP version

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• $\mathcal{N}=2^{\ast }$ Schur indices
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• Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories
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• Higgs Branches of U/SU Quivers via Brane Locking
• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• Conformal Manifolds and 3d Mirrors of $(D_n,D_m)$ Theories
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• Supersymmetry breaking deformations and phase transitions in five dimensions
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• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
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• On low rank 4d $\mathcal{N}=2$ SCFTs
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• Magnetic quivers from brane webs with O7${}^{+}$-planes
• From Regular to Irregular: A Unified Origin for Argyres-Douglas Theories
• FI-flows of 3d N=4 Theories
• Symmetry TFTs from String Theory
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers