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

TL;DR

This paper investigates the mass generation of higher spin fields in AdS_4 via boundary conformal perturbation theory, confirming bulk-boundary correspondence and elucidating gauge symmetry breaking mechanisms.

Contribution

It demonstrates the equivalence of bulk and boundary computations of anomalous dimensions for higher spin fields, supporting the holographic duality in the context of the critical O(N) model.

Findings

Masses of higher spin fields match between bulk and boundary calculations.

Boundary conformal perturbation theory reproduces bulk Witten diagram results.

Supports the interpretation of gauge symmetry breaking via boundary conditions change.

Abstract

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. With this fact our computation provides an additional support for the bulk interpretation.