Holomorphy without Supersymmetry in the Standard Model Effective Field Theory

TL;DR

The paper investigates why the one-loop anomalous dimensions of dimension-six SMEFT operators display a holomorphic structure reminiscent of supersymmetry, despite SMEFT being non-supersymmetric. It classifies the 59 dimension-six operators into holomorphic, anti-holomorphic, and non-holomorphic sectors using complex field strengths and equations of motion, and analyzes the one-loop anomalous-dimension matrix under NDA and flavor symmetry constraints. The main finding is that the weak holomorphy condition holds for the holomorphic block with two Yukawa-proportional violations, while a stronger holomorphy approximation holds for most of the mixing into holomorphic operators; a small number of holomorphy-violating entries tie to the Higgs-gauge sector, leading to relations near the observed Higgs mass, and a recent external explanation supports holomorphy in a key entry. These results hint at a non-accidental, possibly deeper structure in SMEFT RG evolution, motivating exploration of higher-loop behavior or hidden symmetries.

Abstract

The anomalous dimensions of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) respect holomorphy to a large extent. The holomorphy conditions are reminiscent of supersymmetry, even though the SMEFT is not a supersymmetric theory.