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Infrared foundations for quantum geometry. I. Catalog of totally symmetric rank-three field theories

Will Barker1,*, Carlo Marzo2,†, and Alessandro Santoni3,4,‡

  • *Contact author: barker@fzu.cz
  • †Contact author: carlo.marzo@kbfi.ee
  • ‡Contact author: asantoni@uc.cl
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Phys. Rev. D 114, 084098 – Published 30 October, 2026

DOI: https://doi.org/10.1103/xwwb-gnf5

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, which is usually a necessary property of effective field theories in the infrared limit. By comparison, models obtained by other means (tuning couplings and 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, generalizing 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.

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Infrared foundations for quantum geometry. II. Catalog of all torsionlike theories including new ghost-tachyon-free cases

Will Barker, Carlo Marzo, and Alessandro Santoni
Phys. Rev. D 114, 084099 (2026)

Article Text

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Phys. Rev. D 114, 084098– Published 30 October, 2026
  • Received 8 July 2025
  • Accepted 21 August 2026
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