Resolving the pathologies of self-interacting Proca fields: A case study of Proca stars

TL;DR

This paper challenges the notion that self-interacting Proca fields are inherently pathological by demonstrating that their instabilities can be understood as EFT breakdowns, with Proca stars remaining stable in UV completion.

Contribution

It shows that the singularities in self-interacting Proca fields are not fundamental problems but EFT limitations, and that Proca stars can exist beyond EFT instabilities.

Findings

Proca stars persist even after EFT gradient instability.

EFT breakdown occurs before ghost instability.

Heavy degrees of freedom can resolve EFT pathologies.

Abstract

It has been argued that a self-interacting massive vector field is pathological due to a dynamical formation of a singular effective metric of the vector field, which is the onset of a gradient or ghost instability. We discuss that this singularity formation is not necessarily a fundamental problem but a breakdown of the effective field theory (EFT) description of the massive vector field. By using a model of ultraviolet (UV) completion of the massive vector field, we demonstrate that a Proca star, a self-gravitating condensate of the vector field, continues to exist even after the EFT suffers from a gradient instability without any pathology at UV, in which the EFT description is still valid and the gradient instability in EFT may be interpreted as a standard dynamical instability of a high-density boson star from the UV perspective. On the other hand, we find that the EFT description is broken before the ghost instability appears. This suggests that a heavy degree of freedom may be spontaneously excited to cure the pathology of the EFT as the EFT dynamically tends to approach the onset of the ghost instability.