Seiberg-Witten differential via primitive forms

preprint2018arXivOpen access

Abstract

Three-fold quasi-homogeneous isolated rational singularity is argued to define a four dimensional N=2\mathcal{N}=2 SCFT. The Seiberg-Witten geometry is built on the mini-versal deformation of the singularity. We argue in this paper that the corresponding Seiberg-Witten differential is given by the Gelfand-Leray form of K. Saito's primitive form. Our result also extends the Seiberg-Witten solution to include irrelevant deformations.

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