Quartic AdS interactions in higherspin gravity from Conformal Field Theory
Abstract
Clarifying the locality properties of higherspin gravity is a pressing task, but notoriously difficult due to the absence of a weaklycoupled flat regime. The simplest nontrivial case where this question can be addressed is the quartic selfinteraction of the AdS scalar field present in the higherspin multiplet. We investigate this issue in the context of the holographic duality between the minimal bosonic higherspin theory on AdS_{4} and the free O( N) vector model in three dimensions. In particular, we determine the exact explicit form of the derivative expansion of the bulk scalar quartic vertex. The quartic vertex is obtained from the field theory fourpoint function of the operator dual to the bulk scalar, by making use of our previous results for the Witten diagrams of higherspin exchanges. This is facilitated by establishing the conformal block expansions of both the boundary fourpoint function and the dual bulk Witten diagram amplitudes. We show that the vertex we find satisfies a generalised notion of locality.
 Publication:

Journal of High Energy Physics
 Pub Date:
 November 2015
 DOI:
 10.1007/JHEP11(2015)149
 arXiv:
 arXiv:1508.04292
 Bibcode:
 2015JHEP...11..149B
 Keywords:

 Higher Spin Gravity;
 AdSCFT Correspondence;
 Conformal and W Symmetry;
 Higher Spin Symmetry;
 High Energy Physics  Theory
 EPrint:
 40 pages plus appendices, 8 figures