Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases
arXiv:2009.02450 · doi:10.1007/JHEP01(2021)203
Abstract
We study chiral rings of 4d 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.
arXiv comment49 pages; v3: minor corrections
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