Loss of hyperbolicity and tachyons in generalized Proca theories

TL;DR

This paper demonstrates that generalized Proca theories with self-interactions and derivative couplings can experience loss of hyperbolicity and tachyonic instabilities, leading to unphysical behavior during evolution.

Contribution

It extends the analysis of hyperbolicity loss to a broader class of Proca theories with derivative self-interactions, deriving the effective metric and identifying potential instabilities.

Findings

Effective metric can change signature during evolution

Generalized Proca theories can exhibit tachyonic instabilities

Loss of hyperbolicity occurs in broader vector field models

Abstract

Various groups recently demonstrated that the time evolution of simplest self-interacting vector fields, those with self-interaction potentials, can break down after a finite duration in what is called loss of hyperbolicity. We establish that this is not an isolated issue, and other generalizations of the Proca theory suffer from the same problem. Specifically, we show that vector field theories with derivative self-interactions have a similar pathology. For this, we derive the effective metric that governs the dynamics, and show that it can change signature during time evolution. We also show that, generalized Proca theories may suffer from tachyonic instabilities as well, which lead to another form of unphysical behavior.