4d N=2 SCFT from Complete Intersection Singularity

TL;DR

This work develops a geometric framework to classify and study four-dimensional $\mathcal{N}=2$ SCFTs via isolated complete intersection singularities (ICIS). By translating ICIS data into Seiberg-Witten solutions through mini-versal deformations and Jacobi modules, the authors extract the Coulomb branch spectrum and conformal central charges, showing consistent agreement with field-theoretic calculations. A central theme is the presence of exactly marginal deformations, which admit weakly coupled dual frames often realized as affine $D$/$E$ quivers coupled to Argyres-Douglas matter; these frames are used to compute $a$ and $c$ and compare with singularity-based predictions. The results provide strong evidence that the ICIS/singularity approach is a powerful, non-Lagrangian method for classifying and understanding a large class of $4d$ $\mathcal{N}=2$ SCFTs, including nontrivial AD-type theories and Gaiotto-type constructions.

Abstract

Detailed studies of four dimensional N=2 superconformal field theories (SCFT) defined by isolated complete intersection singularities are performed: we compute the Coulomb branch spectrum, Seiberg-Witten solutions and central charges. Most of our theories have exactly marginal deformations and we identify the weakly coupled gauge theory descriptions for many of them, which involve (affine) D and E shaped quiver gauge theories and theories formed from Argyres-Douglas matters. These investigations provide strong evidence for the singularity approach in classifying 4d N=2 SCFTs.

Figures (81)

• Figure 1: Affine $D_5$ quiver from ICIS (1) with $n\in 2{\mathbb Z}$
• Figure 2: $3d$${\mathcal{N}}=4$ mirror of $A_8([1,1,\dots,1],[5,4],[3,3,3])$. The circle nodes denotes $U(n)$ gauge groups and the double circle node denotes an $SU(n)$ gauge group. The balanced nodes are shaded.
• Figure 3: $3d$${\mathcal{N}}=4$ mirror of $A_6([1,1,\dots,1],[4,3],[2,2,2,1])$. The balanced nodes are shaded.
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