4d N=2 SCFT and singularity theory Part I: Classification

Abstract

This is the first of a series of papers in which we systematically use singularity theory to study four dimensional N=2 superconformal field theories. Our main focus in this paper is to identify what kind of singularity is needed to define a SCFT. The constraint for a hypersurface singularity has been found by Sharpere and Vafa, and here the complete set of solutions are listed using a related mathematical result of Stephen S. T. Yau and Yu. We also study other type of singularities such as the complete intersection, quotient of hypersurface singularity by a finite group and non-isolated singularity. We finally conjecture that any three dimensional rational Gorenstein graded isolated singularity should define a N=2 SCFT. We explain how to extract various interesting physical quantities such as Seiberg-Witten geometry, central charges, exact marginal deformations, BPS quiver, RG flow trajectory, etc from the properties of singularity.

52 pages, 7 figures

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Cited by in corpus (21)

• N=1 Deformations and RG Flows of N=2 SCFTs
• Bootstrapping $\mathcal{N}=2$ chiral correlators
• Three dimensional canonical singularity and five dimensional N=1 SCFT
• Chiral algebra of Argyres-Douglas theory from M5 brane
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• M5-brane Sources, Holography, and Argyres-Douglas Theories
• Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated
• Fine Tuning, Sequestering, and the Swampland
• The Singularity Structure of Scale-Invariant Rank-2 Coulomb Branches
• Geometric constraints on the space of N=2 SCFTs II: Construction of special Kähler geometries and RG flows
• Compactifications of 5d SCFTs with a twist
• Argyres-Douglas matter and N=2 dualities
• Infrared enhancement of supersymmetry in four dimensions
• Expanding the landscape of $\mathcal{N}$=2 rank 1 SCFTs
• Infinitely many 4d N=1 SCFTs with a=c
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• On the moduli spaces of 4d $\mathcal{N}=3$ SCFTs I: triple special Kähler structure
• Singularity, Sasaki-Einstein manifold, Log del Pezzo surface and $\mathcal{N}=1$ AdS/CFT correspondence: Part I
• W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras
• Four-dimensional $\mathcal{N}=1$ SCFTs on S-folds with T-branes and AdS/CFT correspondence