Chiral rings, Futaki invariants, plethystics, and Gröbner bases
Open Access
- 29 January 2021
- journal article
- research article
- Published by Springer Science and Business Media LLC in Journal of High Energy Physics
- Vol. 2021 (1), 1-43
- https://doi.org/10.1007/jhep01(2021)203
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 Gröbner basis and plethystic techniques, many non-complete intersections can also be addressed, thus expanding the list of known theories in the literature.
Keywords
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