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We describe solutions of asymptotically AdS$_3$ Einstein gravity that aresourced by the insertion of operators in the boundary CFT$_2$, whose dimensionscales with the central charge of the theory. Previously, we found that thegeometry corresponding to a black hole two-point function is simply related toan infinite covering of the Euclidean BTZ black hole. However, here we findthat the geometry sourced by the presence of a third black hole operator turnsout to be a Euclidean wormhole with two asymptotic boundaries. We constructthis new geometry as a quotient of empty AdS$_3$ realized by domes and doors.The doors give access to the infinite covers that are needed to describe theinsertion of the operators, while the domes describe the fundamental domains ofthe quotient on each cover. In particular, despite the standard fact that theFefferman-Graham expansion is single-sided, the extended bulk geometry containsa wormhole that connects two asymptotic boundaries. We observe that thetwo-sided wormhole can be made single-sided by cutting off the wormhole andgluing on a "Lorentzian cap". In this way, the geometry gives the holographicdescription of a three-point function, up to phases. By rewriting the metric interms of a Liouville field, we compute the on-shell action and find that theresult matches with the Heavy-Heavy-Heavy three-point function predicted by themodular bootstrap. Finally, we describe the geometric transition between doorsand defects, that is, when one or more dual operators describe a conical defectinsertion, rather than a black hole insertion.

Correlation Functions of Huge Operators in AdS$_3$/CFT$_2$: Domes, Doors and Book Pages