Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 11, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP11(2015)149
Keywords
Higher Spin Gravity; AdS-CFT Correspondence; Conformal and W Symmetry; Higher Spin Symmetry
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Funding
- Russian Science Foundation [14-42-00047]
- Lebedev Physical Institute
- DFG [HO 4261/2-1]
- European Science Foundation Holograv network (Holographic methods for strongly coupled systems)
- Russian Science Foundation [14-42-00047] Funding Source: Russian Science Foundation
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Clarifying the locality properties of higher-spin gravity is a pressing task, but notoriously difficult due to the absence of a weakly-coupled flat regime. The simplest non-trivial case where this question can be addressed is the quartic self-interaction of the AdS scalar field present in the higher-spin multiplet. We investigate this issue in the context of the holographic duality between the minimal bosonic higher-spin theory on AdS4 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 four-point function of the operator dual to the bulk scalar, by making use of our previous results for the Witten diagrams of higher-spin exchanges. This is facilitated by establishing the conformal block expansions of both the boundary four-point function and the dual bulk Witten diagram amplitudes. We show that the vertex we find satisfies a generalised notion of locality.
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