# Shift-Symmetric Spin-1 Theories

## TL;DR

This paper explores shift-symmetric massive spin-1 theories in (A)dS space, derived from massive spin-2 theories, revealing new symmetries that influence the nonlinear structure of their decoupling limits.

## Contribution

It introduces a class of shift-symmetric spin-1 theories from massive spin-2 limits, uncovering new symmetries in flat space decoupling limits that constrain their nonlinear interactions.

## Key findings

- Emergence of shift symmetries from massive spin-2 theories.
- Identification of a new symmetry acting on vector modes in flat space.
- Constraints on the scalar-vector sector structure due to the new symmetry.

## Abstract

We study interacting massive spin-1 theories in de Sitter (dS) and anti-de Sitter (AdS) space that possess shift symmetries parametrized by (A)dS Killing vectors. We show how they emerge from the massless limit of massive spin-2 theories on (A)dS space. In the case of massive gravity, the corresponding spin-1 theory realizes a symmetry breaking pattern that takes two copies of the (A)dS isometry group down to a diagonal subgroup. By taking the flat space limit of this theory, we find a new symmetry of the decoupling limit of massive gravity in flat space. This symmetry acts on the vector modes, is parametrized by an antisymmetric tensor, and fixes the nonlinear structure of the scalar-vector sector of the decoupling limit.