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 AdS3, 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.
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Hulík, O., Procházka, T. & Raeymaekers, J. Multi-centered AdS3 solutions from Virasoro conformal blocks. J. High Energ. Phys. 2017, 129 (2017). https://doi.org/10.1007/JHEP03(2017)129
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DOI: https://doi.org/10.1007/JHEP03(2017)129