..., 83106786, 114382724, 1509048322, 2343463290, 27410087742, ... Efficient Hilbert Series for Effective Theories

Abstract

We present an efficient algorithm for determining the Hilbert series of an effective theory and provide a companion code called ECO (Efficient Counting of Operators) in FORM. For example, the Hilbert series for the dimension 15 operators in the Standard Model Effective Theory (SMEFT) can be obtained in a minute on a single CPU core. While our implementation focusses on SMEFT, we allow for a flexible user input of the light degrees of freedom. Furthermore, gravity, as well as additional U(1) global or gauge symmetries can be included.

9 pages, no figures, FORM files included

References in corpus (6)

• Counting Gauge Invariants: the Plethystic Program
• Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators
• Operator bases, $S$-matrices, and their partition functions
• Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
• Highest Weight Generating Functions for Hilbert Series
• FORM version 4.2

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• Counting Operators in $N=1$ Supersymmetric Gauge Theories
• Dimension-eight Operator Basis for Universal Standard Model Effective Field Theory
• Froggatt-Nielsen Meets the SMEFT
• Custodial Symmetry (Violation) in SMEFT
• Extending low energy effective field theory with a complete set of dimension-7 operators
• Two-loop dimension Six Effective Action: Integrating Out Heavy Scalar