Multi-centered higher spin solutions from W N $$ {\mathcal{W}}_N $$ 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 A N − 1 $$ {{\mathcal{A}}_N}_{-1} $$ 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 W N $$ {\mathcal{W}}_N $$ vacuum conformal block at large central charge. Therefore, knowledge of the W N $$ {\mathcal{W}}_N $$ vacuum block determines the multi-centered solution. Our calculations go beyond the heavy-light approximation by including the backreaction of all higher spin particles.

Keywords

• AdS-CFT Correspondence
• Chern-Simons Theories
• Conformal and W Symmetry
• Higher Spin Gravity