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

Dan Xie Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43558

arXiv preprint arXiv:1510.01324, 2015.10
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 ST 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.
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  title={4d N= 2 SCFT and singularity theory Part I: Classification},
  author={Dan Xie, and Shing-Tung Yau},
  booktitle={arXiv preprint arXiv:1510.01324},
Dan Xie, and Shing-Tung Yau. 4d N= 2 SCFT and singularity theory Part I: Classification. 2015. In arXiv preprint arXiv:1510.01324. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204036572777122.
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