Multi-centered AdS$_3$ solutions from Virasoro conformal blocks

TL;DR

This paper constructs multi-centered AdS$_3$ gravity solutions using classical Virasoro conformal blocks, linking particle backreaction to Liouville theory and conformal monodromy problems, revealing new asymmetric configurations in the dual CFT.

Contribution

It introduces a novel method to build multi-centered AdS$_3$ solutions via Virasoro conformal blocks and Liouville theory, connecting gravity solutions to conformal field theory techniques.

Findings

Constructed explicit multi-centered solutions using conformal blocks.

Linked particle backreaction in AdS$_3$ to monodromy problems in Liouville theory.

Demonstrated solutions correspond to asymmetric operator configurations in the dual CFT.

Abstract

We revisit the construction of multi-centered solutions in three-dimensional anti-de Sitter gravity in the light of the recently discovered connection between particle worldlines and classical Virasoro conformal blocks. We focus on multi-centered solutions which represent the backreaction of point masses moving on helical geodesics in global AdS$_3$, and argue that their construction reduces to a problem in Liouville theory on the disk with Zamolodchikov-Zamolodchikov boundary condition. In order to construct the solution one needs to solve a certain monodromy problem which we argue is solved by a vacuum classical conformal block on the sphere in a particular channel. In this way we construct multi-centered gravity solutions by using conformal blocks special functions. We show that our solutions represent left-right asymmetric configurations of operator insertions in the dual CFT. We also provide a check of our arguments in an example and comment on other types of solutions.