We develop the representation of bulk fields with spin one and spin two in anti-de Sitter space, as non-local observables in the dual CFT. Working in holographic gauge in the bulk, at leading order in 1/N bulk gauge fields are obtained by smearing boundary currents over a sphere on the complexified boundary, while linearized metric fluctuations are obtained by smearing the boundary stress tensor over a ball. This representation respects AdS covariance up to a compensating gauge transformation. We also consider massive vector fields, where the bulk field is obtained by smearing a non-conserved current. We compute bulk two-point functions and show that bulk locality is respected. We show how to include interactions of massive vectors using 1/N perturbation theory, and we comment on the issue of general backgrounds.
Kabat, D.N., Lifschytz, G., Roy, S., & Sarkar, D. (2012). Holographic representation of bulk fields with spin in AdS/CFT. Report NSF-KITP-12-045 DOI: 10.1103/PhysRevD.86.026004