Constructing effective field theories via their harmonics

TL;DR

This work recasts EFT operator construction as harmonic analysis on the kinematic Grassmannian $G_2(\\mathbb{C}^N)$, where observables decompose into conformal-primary harmonics identified by the special conformal generator $K$. By organizing spinor-helicity data into $U(N)$ representations via Young diagrams and labeling states with semi-standard Young tableaux, it provides a systematic, primary-based basis for the $S$-matrix that automatically respects on-shell and EOM/IBP constraints. The authors supply explicit low-mass-dimension spectra up to $\\Delta\\le 6$, including holomorphic and non-holomorphic sectors for $N=3$ and $N=4$, illustrating how derivatives and IBP shape the harmonic content. They discuss the implications for operator mixing, non-renormalization structures, and potential connections to positivity bounds and amplitude bases, outlining future avenues to apply this mathematically structured basis to phenomenology and non-perturbative approaches.

Abstract

We consider the construction of operator bases for massless, relativistic quantum field theories, and show this is equivalent to obtaining the harmonic modes of a physical manifold (the kinematic Grassmannian), upon which observables have support. This enables us to recast the approach of effective field theory (EFT) through the lens of harmonic analysis. We explicitly construct harmonics corresponding to low mass dimension EFT operators.

Figures (1)

• Figure 1: Young diagram for the harmonic modes of the Grassmannian.