Inconsistencies of Massive Charged Gravitating Higher Spins

TL;DR

This work addresses the inconsistencies of massive charged higher-spin fields interacting with electromagnetism and gravity, focusing on causality and degrees of freedom (DoF). It shows that for ${s=3/2}$, dynamical gravity can improve causality bounds, producing ${m}$– and ${\Lambda}$-dependent phase structures in the ${ (m^2,\, \Lambda) }$ plane, with true causal propagation requiring Planck-scale masses ${m^2\gtrsim {2e^2}/{\kappa^2}}$, and links these improvements to softly broken ${\cal N}=2$ cosmological SUGRA. For spins ${s\ge 2}$, DoF constraints dominate and no DoF-preserving coupling to electromagnetism and gravity appears available in general backgrounds; in particular, the ${s=2}$ case admits only a unique ${g=1/2}$ DoF-preserving EM coupling, but remains acausal, and there is no tree-unitary theory. Overall, the results suggest that a consistent effective description of massive higher spins in realistic backgrounds likely requires a UV completion with an extended spectrum (e.g., a Regge tower), rather than a finite local field theory for a single higher-spin particle.

Abstract

We examine the causality and degrees of freedom (DoF) problems encountered by charged, gravitating, massive higher spin fields. For spin s=3/2, making the metric dynamical yields improved causality bounds. These involve only the mass, the product eM_P of the charge and Planck mass and the cosmological constant Λ. The bounds are themselves related to a gauge invariance of the timelike component of the field equation at the onset of acausality. While propagation is causal in arbitrary E/M backgrounds, the allowed mass ranges of parameters are of Planck order. Generically, interacting spins s>3/2 are subject to DoF violations as well as to acausality; the former must be overcome before analysis of the latter can even begin. Here we review both difficulties for charged s=2 and show that while a g-factor of 1/2 solves the DoF problem, acausality persists for any g. Separately we establish that no s=2 theory --DoF preserving or otherwise -- can be tree unitary.

Figures (3)

• Figure 1: Phase diagram for neutral, massive $s=3/2$ in cosmological backgrounds.
• Figure 2: Phase diagram for charged, massive $s=3/2$ coupled to cosmological Einstein--Maxwell backgrounds.
• Figure 3: Phase diagram for charged, massive $s=3/2$ with SUGRA-inspired non-minimal coupling to cosmological Maxwell--Einstein backgrounds.