Shift Symmetries and AdS/CFT

TL;DR

This paper investigates how shift symmetries of massive fields in AdS space are manifested in the dual CFT, revealing gauge symmetry realization in alternate quantization and integral Ward identities in standard quantization.

Contribution

It elucidates the realization of AdS shift symmetries in the boundary CFT, connecting bulk gauge symmetries to boundary Ward identities across different quantization schemes.

Findings

Shift symmetry corresponds to gauge symmetry in the dual CFT under alternate quantization.

In standard quantization, shift symmetry leads to integral Ward identities.

The analysis clarifies the boundary manifestation of bulk shift symmetries.

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.