Inconsistencies of Massive Charged Gravitating Higher Spins

TL;DR

This paper investigates the causality and degrees of freedom issues in charged, massive higher spin fields interacting with gravity, revealing fundamental limitations and conditions for causality and unitarity across different spins.

Contribution

It provides a detailed analysis of causality bounds and DoF problems for higher spins, especially s=3/2 and s=2, highlighting the persistent challenges and potential solutions.

Findings

Causality bounds depend on charge, mass, and cosmological constant.

For spin 3/2, dynamical metrics improve causality bounds.

Spin 2 theories face DoF violations and acausality issues, unaffected by g-factor adjustments.

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 \Lambda. 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.