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Chiral rings, Futaki invariants, plethystics, and Grobner bases

Bao, J. ORCID: 0000-0002-9583-1696, He, Y. ORCID: 0000-0002-0787-8380 & Xiao, Y. (2021). Chiral rings, Futaki invariants, plethystics, and Grobner bases. Journal of High Energy Physics, 2021(1), article number 203. doi: 10.1007/jhep01(2021)203


We study chiral rings of 4d 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.

Publication Type: Article
Additional Information: This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Publisher Keywords: Conformal Field Theory, Differential and Algebraic Geometry, Global Symmetries
Subjects: Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
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