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

TL;DR

This paper analyzes the boundary terms of free higher-spin gauge fields in AdS space, revealing gauge symmetry breaking for spins > 2 and connecting bulk actions to boundary conformal higher-spin fields.

Contribution

It determines the boundary terms for higher-spin fields in AdS, showing the impossibility of full gauge invariance for spins greater than two and relating bulk and boundary theories.

Findings

No local boundary term restores full gauge symmetry for spins > 2

Broken symmetry corresponds to higher-spin Weyl transformations

Boundary action relates on-shell bulk action to boundary conformal higher-spin fields

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.