The Hilbert series of U/SU SQCD and Toeplitz Determinants

Abstract

We present a new technique for computing Hilbert series of N=1 supersymmetric QCD in four dimensions with unitary and special unitary gauge groups. We show that the Hilbert series of this theory can be written in terms of determinants of Toeplitz matrices. Applying related theorems from random matrix theory, we compute a number of exact Hilbert series as well as asymptotic formulae for large numbers of colours and flavours -- many of which have not been derived before.

49 pages, 6 figures. Version 2: references added

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Cited by in corpus (14)

• Low-derivative operators of the Standard Model effective field theory via Hilbert series methods
• Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
• On the impact of dimension-eight SMEFT operators on Higgs measurements
• Complete Intersection Moduli Spaces in N=4 Gauge Theories in Three Dimensions
• Flavor Invariants and Renormalization-group Equations in the Leptonic Sector with Massive Majorana Neutrinos
• Hilbert Series, Machine Learning, and Applications to Physics
• The Hilbert series of N=1 SO(N_c) and Sp(N_c) SQCD, Painlevé VI and Integrable Systems
• Exact equivalences and phase discrepancies between random matrix ensembles
• Constructing Operator Basis in Supersymmetry: A Hilbert Series Approach
• New results for the SQCD Hilbert series
• Counting Operators in $N=1$ Supersymmetric Gauge Theories
• Moduli space of supersymmetric QCD in the Veneziano limit
• Crystal bases and three-dimensional $\mathcal{N}=4$ Coulomb branches
• On the Chiral Ring and Vacua of $\mathcal{N}=1$ Adjoint SQCD