Infrared foundations for quantum geometry I: Catalogue of totally symmetric rank-three field theories

TL;DR

This paper systematically classifies all linear, gauge-invariant models for totally symmetric rank-three fields in flat spacetime, identifying foundational models that propagate specific massless particles without instabilities.

Contribution

It introduces a new algorithm based on Wigner decomposition to detect symmetric models, extending previous analyses and enabling the classification of stable, gauge-invariant rank-three field theories.

Findings

Found models propagate one or both massless particles of spin one or three.

Identified no-ghost-no-tachyon constraints for the models.

Established existence of foundational models with specific particle content.

Abstract

We systematically obtain all linear models which propagate a totally symmetric rank-three field without parity violation on a flat background. Each such model is defined exclusively by its gauge symmetry, a necessary property of effective field theories in the infrared limit. By comparison, models obtained by other means (tuning couplings or cherry-picking operators) may be unstable against radiative corrections. For each model, we compute the spectrum of massless and massive particles, and the no-ghost-no-tachyon constraints on the couplings. We conclude that foundational models exist which can propagate one massless particle of spin one or spin three in isolation, or both particles simultaneously, generalising the model of Campoleoni and Francia. Our algorithm for detecting symmetric models is grounded in particle physics methods, being based directly on the Wigner decomposition of the field. Compared to our recent analysis of the totally symmetric rank-three field (whose results we confirm and extend) our new algorithm does not require an ansatz for the symmetry transformation, and is not restricted to so-called 'free' symmetries.