The problem with Proca: ghost instabilities in self-interacting vector fields

TL;DR

This paper demonstrates that adding self-interactions to Proca vector fields introduces ghost instabilities, which cannot be avoided by nonperturbative effects, impacting models of vector dark matter and photon interactions.

Contribution

It shows that self-interacting Proca fields inherently develop ghost instabilities, challenging previous assumptions about their stability and viability in physical models.

Findings

Self-interactions cause ghost instabilities in Proca fields.

Instabilities are triggered during superradiance on Kerr backgrounds.

Nonperturbative dynamics do not prevent the instabilities.

Abstract

Massive vector fields feature in several areas of particle physics, e.g., as carriers of weak interactions, dark matter candidates, or as an effective description of photons in a plasma. Here we investigate vector fields with self-interactions by replacing the mass term in the Proca equation with a general potential. We show that this seemingly benign modification inevitably introduces ghost instabilities of the same kind as those recently identified for vector-tensor theories of modified gravity (but in this simpler, minimally coupled theory). It has been suggested that nonperturbative dynamics may drive systems away from such instabilities. We demonstrate that this is not the case by evolving a self-interacting Proca field on a Kerr background, where it grows due to the superradiant instability. The system initially evolves as in the massive case, but instabilities are triggered in a finite time once the self-interaction becomes significant. These instabilities have implications for the formation of condensates of massive, self-interacting vector bosons, the possibility of spin-one bosenovae, vector dark matter models, and effective models for interacting photons in a plasma.