Boundary action of free AdS higher-spin gauge fields and the holographic correspondence

Abstract

We determine the boundary terms of the free higher-spin action which reproduce the AdS Fronsdal equations in an AdS manifold with a finite distance boundary. The boundary terms are further constrained by the gauge invariance of the total action. We show that, for spins larger than two, no local boundary term can restore the full gauge symmetry, and the broken symmetry corresponds to higher-spin Weyl transformations on the boundary CFT. The boundary action is used for the evaluation of the on-shell higher-spin AdS action in terms of the boundary data given by a conformal higher-spin field.