Abstract
We consider higher-spin gravity in (Euclidean) AdS4, dual to a free vector model on the 3d boundary. In the bulk theory, we study the linearized version of the Didenko-Vasiliev black hole solution: a particle that couples to the gauge fields of all spins through a BPS-like pattern of charges. We study the interaction between two such particles at leading order. The sum over spins cancels the UV divergences that occur when the two particles are brought close together, for (almost) any value of the relative velocity. This is a higher-spin enhancement of supergravity’s famous feature, the cancellation of the electric and gravitational forces between two BPS particles at rest. In the holographic context, we point out that these “Didenko-Vasiliev particles” are just the bulk duals of bilocal operators in the boundary theory. For this identification, we use the Penrose transform between bulk fields and twistor functions, together with its holographic dual that relates twistor functions to boundary sources. In the resulting picture, the interaction between two Didenko-Vasiliev particles is just a geodesic Witten diagram that calculates the correlator of two boundary bilocals. We speculate on implications for a possible reformulation of the bulk theory, and for its non-locality issues.
Highlights
From a complementary point of view, HS gravity is a larger sibling of supergravity, the low-energy limit of string theory
There, we evaluate the linearized bulk fields that correspond to a bilocal operator in the boundary CFT, and notice that they coincide with the fields of a DV particle
We saw that a boundary bilocal operator generates a bulk DV particle that travels along the geodesic between the two boundary points, and carries HS charges that source the bulk HS gauge fields; the correlator of two boundary bilocals can be expressed as the exchange of HS fields between the two bulk DV particles
Summary
The theory of linearized higher-spin gauge fields on maximally symmetric spacetimes, with or without cosmological constant, was put forward by Fronsdal in [18, 19]. A spin-s gauge potential in Fronsdal’s formulation is given by a tensor hμ1...μs that is totally symmetric and double-traceless in its indices: hμ1...μs = h(μ1...μs) ; hνν ρ ρμ. A spin-s gauge potential in Fronsdal’s formulation is given by a tensor hμ1...μs that is totally symmetric and double-traceless in its indices: hμ1...μs = h(μ1...μs) ; hνν ρ ρμ1 The first of these constraints becomes non-trivial for s ≥ 2, and the second — for s ≥ 4. One can construct from hμ1...μs a gauge-invariant second-derivative object, known as the Fronsdal tensor
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