Shift Symmetries and AdS/CFT

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. The shift symmetry is preserved in the alternate quantization scheme in which the dual conformal field gets the smaller $\Delta_-$ conformal dimension, while in the standard quantization scheme the shift symmetry is broken. The shift symmetry is realized as a gauge symmetry in the dual CFT, so that only shift invariant operators are true conformal primary fields.Comment: 38 pages, 1 figur