# Shift symmetry At special values of the mass (or conformal dimension), massive fields in AdS have a **shift symmetry**. This symmetry becomes a gauge symmetry in the CFT. In dS${}_D$ with radius $1/H$, a massive scalar field has shift symmetries for masses$m_k^2=-k(k+D-1) H^2, \quad k=0,1,2, \ldots$where $k$ is called the level. Even though the fields are tachyonic for $k>0$, they correspond to unitary irreducible representations of the de Sitter group if the shift symmetries are gauged. ## Refs - [[2018#Bonifacio, Hinterbichler, Joyce, Rosen]]: shift symmetry for all spins in dS and AdS - [[2022#Blauvelt, Engelbrecht, Hinterbichler]]: shift symmetry and AdS/CFT - [[2023#Bonifacio, Hinterbichler]]: fermions in AdS - [[2024#Hinterbichler]]: all field types