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# Advances in Theoretical and Mathematical Physics

## Volume 21 (2017)

### Number 3

### $4d$ $\mathcal{N} = 2$ SCFT from complete intersection singularity

Pages: 801 – 855

DOI: http://dx.doi.org/10.4310/ATMP.2017.v21.n3.a6

#### Authors

#### Abstract

Detailed studies of four dimensional $\mathcal{N} = 2$ 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 $4d$ $\mathcal{N} = 2$ SCFTs.

YW is supported in part by the U.S. Department of Energy under grant Contract Number DE-SC00012567. The work of DX is supported by Center for Mathematical Sciences and Applications at Harvard University, and in part by the Fundamental Laws Initiative of the Center for the Fundamental Laws of Nature, Harvard University. The work of S.T Yau is supported by NSF grant DMS-1159412, NSF grant PHY- 0937443, and NSF grant DMS-0804454. The work of Stephen Yau is supported by NSFC (grant nos. 11401335, 11531007) and Tsinghua University Initiative Scientific Research Program.