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.
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Hulík, O., Raeymaekers, J. & Vasilakis, O. Multi-centered higher spin solutions from \( {\mathcal{W}}_N \) conformal blocks. J. High Energ. Phys. 2018, 101 (2018). https://doi.org/10.1007/JHEP11(2018)101
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DOI: https://doi.org/10.1007/JHEP11(2018)101