Abstract
Motivated by the question of bulk localization in holography, we study the problem of constructing multi-centered solutions in higher spin gravity which describe point particles in the interior of AdS3. In the Chern-Simons formulation these take into account the backreaction after adding Wilson line sources. We focus on chiral solutions where only the left-moving sector is excited. In that case it is possible to choose a gauge where the dynamical variables are a set of Toda fields living in the bulk. The problem then reduces to solving the {{mathcal{A}}_N}_{-1} Toda equations with delta function sources, which in turn requires solving an associated monodromy problem. We show that this monodromy problem is equivalent to the monodromy problem for a particular {mathcal{W}}_N vacuum conformal block at large central charge. Therefore, knowledge of the {mathcal{W}}_N vacuum block determines the multi-centered solution. Our calculations go beyond the heavy-light approximation by including the backreaction of all higher spin particles.
Highlights
The question of how local bulk physics in anti-de-Sitter space emerges holographically from the boundary CFT is an important one and has received considerable attention in recent years following the work of HKKL [1]
Motivated by the question of bulk localization in holography, we study the problem of constructing multi-centered solutions in higher spin gravity which describe point particles in the interior of AdS3
We show that this monodromy problem is equivalent to the monodromy problem for a particular WN vacuum conformal block at large central charge
Summary
The question of how local bulk physics in anti-de-Sitter space emerges holographically from the boundary CFT is an important one and has received considerable attention in recent years following the work of HKKL [1]. The goal of the current work is to generalize the above results to the construction of multi-centered solutions in higher spin gravity theories, coming from backreacting particles with higher spin charges This problem was analyzed in [10, 11] in the heavy-light limit. To summarize our results in the context of bulk locality, we provide in this work a prescription to construct a state in the Lorentzian bulk theory containing localized particles from a classical block in a Euclidean Toda CFT. The present work can presumably be viewed as a concrete realization of this idea, albeit in a highly symmetric setting
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