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K stability and stability of chiral ring

Tristan C Collins Dan Xie Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43622

arXiv preprint arXiv:1606.09260, 2016.6
We define a notion of stability for chiral ring of four dimensional N= 1 theory by introducing test chiral rings and generalized a maximization. We conjecture that a chiral ring is the chiral ring of a superconformal field theory if and only if it is stable. We then study N= 1 field theory derived from D3 branes probing a three-fold singularity X, and show that the K stability which implies the existence of Ricci-flat conic metric on X is equivalent to the stability of chiral ring of the corresponding field theory.
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@inproceedings{tristan2016k,
  title={K stability and stability of chiral ring},
  author={Tristan C Collins, Dan Xie, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204512137545186},
  booktitle={arXiv preprint arXiv:1606.09260},
  year={2016},
}
Tristan C Collins, Dan Xie, and Shing-Tung Yau. K stability and stability of chiral ring. 2016. In arXiv preprint arXiv:1606.09260. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204512137545186.
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