# Shift Symmetries in (Anti) de Sitter Space

## TL;DR

This paper develops extended shift symmetries for all integer spin fields in (A)dS space, generalizing flat space symmetries and exploring their implications for interactions and higher-spin theories.

## Contribution

It introduces a new class of shift symmetries for tensor fields in (A)dS space, extending known flat space symmetries to curved backgrounds and analyzing their role in interactions.

## Key findings

- Constructed shift symmetries for all integer spins in (A)dS.
- Extended the special galileon symmetry to (A)dS space.
- Discussed potential for interacting massive higher-spin particles.

## Abstract

We construct a class of extended shift symmetries for fields of all integer spins in de Sitter (dS) and anti-de Sitter (AdS) space. These generalize the shift symmetry, galileon symmetry, and special galileon symmetry of massless scalars in flat space to all symmetric tensor fields in (A)dS space. These symmetries are parametrized by generalized Killing tensors and exist for fields with particular discrete masses corresponding to the longitudinal modes of massive fields in partially massless limits. We construct interactions for scalars that preserve these shift symmetries, including an extension of the special galileon to (A)dS space, and discuss possible generalizations to interacting massive higher-spin particles.