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.

We show that interpreting the inverse AdS 3 radius 1/l as a Grassmann variable results in a formal map from gravity in AdS 3 to gravity in flat space. The underlying reason for this is the fact that ISO(2, 1) is the Inonu-Wigner contraction of SO(2, 2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS 3 maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS 3 case. Our results straightforwardly generalize to the higher spin case: the recently constructed flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We conclude with a discussion of singularity resolution in the BMS gauge as an application.

It is possible to formulate fluid dynamics in terms of group-valued variables. This is particularly suited to the cases where the fluid has nonabelian charges and is coupled to nonabelian gauge fields. We explore this formulation further in this paper. An action for a fluid of relativistic particles (with and without spin) is given in terms of the Lorentz and Poincaré (or de Sitter) groups. Considering the case of particles with flavor symmetries, a general fluid action which also incorporates all flavor anomalies is given. The chiral magnetic and chiral vorticity effects as well as the consequences of the mixed gauge-gravity anomaly are discussed.