Pathology of self-interacting vectors*

Various groups have recently shown that theories of vector fields with couplings beyond the Proca mass, i.e., self-interacting vectors, are pathological. The problem manifests when the field norm reaches high-but-finite values, beyond which well-posed time evolution ceases to exist. The underlying reason is that the dynamics of the field is not governed by the spacetime metric, but by an effective one. The latter metric depends on the vector field itself, hence can become singular even when the spacetime is regular. This result suggests a reevaluation of fundamental theories that features such vector fields, which are numerous in gravity and cosmology. We will detail the underlying reason for the ill-posed behavior and the subtleties in its identification. We will also discuss how it can be avoided using an effective field theory picture.