Seiberg-Witten differential via primitive forms

TL;DR

This paper connects the Seiberg-Witten differential in 4D $ abla=2$ SCFTs to Gelfand-Leray forms of primitive forms associated with three-fold rational singularities, extending the solution to irrelevant deformations.

Contribution

It demonstrates that the Seiberg-Witten differential can be expressed as a Gelfand-Leray form of primitive forms, broadening the understanding of deformations in SCFTs.

Findings

Seiberg-Witten differential equals Gelfand-Leray form of primitive form

Extension of Seiberg-Witten solutions to include irrelevant deformations

Application to three-fold quasi-homogeneous isolated rational singularities

Abstract

Three-fold quasi-homogeneous isolated rational singularity is argued to define a four dimensional $\mathcal{N}=2$ 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.