Multi-centered higher spin solutions from $W_N$ conformal blocks

TL;DR

This paper constructs multi-centered higher spin gravity solutions in AdS3 using $ ext{W}_N$ conformal blocks, linking bulk solutions to boundary monodromy problems and including full backreaction effects.

Contribution

It establishes a novel connection between multi-centered higher spin solutions and $ ext{W}_N$ conformal blocks, extending beyond the heavy-light approximation.

Findings

Multi-centered solutions are characterized by $ ext{W}_N$ vacuum blocks.

The monodromy problem encodes the backreaction of higher spin particles.

Results include solutions with full backreaction, not limited to approximations.

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 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 $\mathcal{A}_{N-1}$ 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.