Shift Symmetries and AdS/CFT

Abstract: Massive fields on anti-de Sitter (AdS) space enjoy galileon-like shift symmetries at particular values of their masses. We explore how these shift symmetries are realized through the boundary conformal field theory (CFT), at the level of the 2-point functions. In the alternate quantization scheme in which the dual conformal field gets the smaller $\Delta_-$ conformal dimension, the shift symmetry is realized as a gauge symmetry in the dual CFT, so that only shift invariant operators are true conformal primary fields. In the standard quantization scheme the shift symmetry acts on the source, leading to Ward identities that take the form of integral constraints.