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arXiv · 2009.02450

Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases

Jiakang Bao·Yang-Hui He·Yan Xiao
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Abstract

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 Gr\"obner basis and plethystic techniques, many non-complete intersections can also be addressed, thus expanding the list of known theories in the literature.

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Jiakang Bao, Yang-Hui He, Yan Xiao. 2020-09-05. Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases. https://doi.org/10.1007/jhep01(2021)203

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