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Multi-centered higher spin solutions from WN conformal blocks
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DOI：10.1007/JHEP11(2018)101.png)
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Abstract
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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 AdS(3). 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 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 W-N vacuum conformal block at large central charge. Therefore, knowledge of the 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.
Keywords:
AdS-CFT Correspondence
Chern-Simons Theories
Conformal and W Symmetry
Higher Spin Gravity
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