论文标题
手性戒指，futaki不变性，庞大的遗传和格罗布纳基地
Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases
论文作者
论文摘要
我们通过K稳定性的概念研究4D $ \ MATHCAL {N} = 1 $超对称规格理论的手性环。我们表明，当使用Hilbert系列执行Futaki不变性的计算时，仅在前者的分母中仅包含测试对称信息就不足。我们讨论了一种修改分子的方法，以便可以正确确定K稳定性，并还采用了重新缩放方法来简化涉及测试配置的计算。通过考虑各种理论的真空模量空间，用许多示例来说明所有这些。使用Gröbner的基础和庞大的技术，也可以解决许多不完整的交集，从而扩大了文献中已知理论的列表。
We study chiral rings of 4d $\mathcal{N}=1$ supersymmetric gauge theories via the notion of K-stability. We show that when using Hilbert series to perform the computations of Futaki invariants, it is not enough to only include the test symmetry information in the former's denominator. We discuss a way to modify the numerator so that K-stability can be correctly determined, and a rescaling method is also applied to simplify the calculations involving test configurations. All of these are illustrated with a host of examples, by considering vacuum moduli spaces of various theories. Using Gröbner basis and plethystic techniques, many non-complete intersections can also be addressed, thus expanding the list of known theories in the literature.
