The intrinsic pathology of self-interacting vector fields

TL;DR

Self-interacting vector field theories can exhibit unphysical behavior intrinsically, even without external coupling, raising concerns for their use in various physics domains and necessitating tools for their identification.

Contribution

The paper reveals an inherent unphysical behavior in self-interacting vector fields and introduces a framework to identify and analyze this issue.

Findings

Unphysical behavior occurs in vector theories without external coupling.

Development of tools to detect ill-defined evolution in vector fields.

Highlights risks for cosmology and high energy physics models.

Abstract

We show that self-interacting vector field theories exhibit unphysical behaviour even when they are not coupled to any external field. This means any theory featuring such vectors is in danger of being unphysical, an alarming prospect for many proposals in cosmology, gravity, high energy physics and beyond. The problem arises when vector fields with healthy configurations naturally reach a point where time evolution is mathematically ill-defined. We develop tools to easily identify this issue, and provide a simple and unifying framework to investigate it.