Multi-centered higher spin solutions from $$ {\mathcal{W}}_N $$ conformal blocks

Abstract

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 $$ {{\mathcal{A}}_N}_{-1} $$ 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 $$ {\mathcal{W}}_N $$ W N vacuum conformal block at large central charge. Therefore, knowledge of the $$ {\mathcal{W}}_N $$ 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.