The masses of higher spin fields on AdS_4 and conformal perturbation theory

Understand

We study the breaking of gauge symmetry for higher spin theory on AdS_4 dual to the 3d critical O(N) vector model.

• It was argued that the breaking is due to the change of boundary condition for a scalar field through a loop effect and the Goldstone modes are bound states of a scalar field and higher spin field.
• The masses of higher spin fields were obtained from the anomalous dimensions of dual currents at the leading order in 1/N, and we reproduce them from the O(N) vector model in the conformal perturbation theory.
• The anomalous dimensions can be computed from the bulk theory using Witten diagrams, and we show that the bulk computation reduces to the boundary one in the conformal perturbation theory.