Abstract
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.
Highlights
In this article we propose to initiate a systematic study starting from the reasonable assumption that the HS theory can be described as a series in the coupling constant with the first term being the free Fronsdal action [44]
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
As we showed in the previous section, the addition of a local couterterm allows the recovery of the full bulk gauge symmetry if d > 2
Summary
We first recall the AdS Fronsdal HS equations and action in order to explicit our notations. M2s is given by m2s = s2 + (d − 5) s − 2(d − 2) Using these notations for the fields and EOM, we express the action of the free massless spin s field in the region z ≥ zB of AdSd+1 denoted in the following by M: IM. This Fronsdal action is our starting point to construct the boundary terms which allow to derive the EOM from the variational principle and which insure that the total action is invariant under the largest subset of gauge transformations. The gauge invariance of the Fronsdal action in AdS is due to the Bianchi identity:
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