A Model Independent Ultraviolet Cutoff for Theories with Charged Massive Higher Spin Fields

TL;DR

The paper establishes a model-independent intrinsic ultraviolet cutoff for theories of charged massive higher-spin fields in flat space, showing that the cutoff scales as $\Lambda_s = {\cal O}\left(m\,e^{-1/(2s-1)}\right)$ for spin $s$. Using the Stückelberg formalism, the authors analyze spins 2, 3, 3/2, and 5/2, derive the structure of non-renormalizable operators, and demonstrate that field redefinitions or adding non-minimal local terms cannot raise the bound. They provide explicit results for low spins ($\Lambda_2 = m e^{-1/3}$, $\Lambda_3 = m e^{-1/5}$, $\Lambda_{3/2} = m/\sqrt{e}$, $\Lambda_{5/2} = m e^{-1/4}$) and then generalize to arbitrary spin via a cohomological obstruction argument, with a universal scaling pattern. The work highlights how fundamental limitations on the high-energy consistency of higher-spin charged theories interface with UV completions and causality, and suggests that stronger bounds may arise from external-field causality or nonlocal UV completions.

Abstract

We argue that the theory of a massive higher spin field coupled to electromagnetism in flat space possesses an intrinsic, model independent, finite upper bound on its UV cutoff. By employing the Stueckelberg formalism we do a systematic study to quantify the degree of singularity of the massless limit in the cases of spin 2, 3, 3/2, and 5/2. We then generalize the results for arbitrary spin to find an expression for the maximum cutoff of the theory as a function of the particle's mass, spin, and electric charge. We also briefly explain the physical implications of the result and discuss how it could be sharpened by use of causality constraints.