# Galileon-like vector fields

## TL;DR

This paper introduces vector field theories with second derivatives that produce second order equations, extending Galileon models to vector fields and exploring their stability and energy conditions.

## Contribution

It constructs vector field Lagrangians with second derivatives leading to second order equations, generalizing Galileons beyond scalar fields.

## Key findings

- Identifies stable, ghost-free backgrounds without gauge invariance.
- Examples include backgrounds that violate the Null Energy Condition.
- Extends the construction to include dynamical gravity.

## Abstract

We construct simple Lagrangians of vector fields which involve second derivatives, but nevertheless lead to second order field equations. These vector fields are, therefore, analogs of generalized Galileons. Our construction is given first in Minkowski space, and then generalizied to include dynamical gravity. We present examples of backgrounds that are stable and ghost-free despite the absence of gauge invariance. Some of these backgrounds violate the Null Energy Condition.