..., 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, which counts the number of operators with a specific field content, 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.