City Research Online

Chiral rings, Futaki invariants, plethystics, and Grobner bases

Bao, J. ORCID: 0000-0002-9583-1696, He, Y. ORCID: 0000-0002-0787-8380 and Xiao, Y. (2021). Chiral rings, Futaki invariants, plethystics, and Grobner bases. Journal of High Energy Physics, 2021, 203.. doi: 10.1007/JHEP01(2021)203

Abstract

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 Mathematics, Computer Science & Engineering > Mathematics
Date available in CRO: 26 Apr 2021 09:04
Date deposited: 23 April 2021
Date of acceptance: 19 December 2020
Date of first online publication: 29 January 2021
URI: https://openaccess.city.ac.uk/id/eprint/25957
[img]
Preview
Text - Published Version
Available under License Creative Commons: Attribution International Public License 4.0.

Download (752kB) | Preview

Export

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login