Worldline approach to semi-classical conformal blocks

Understand

We extend recent results on semi-classical conformal blocks in 2d CFT and their relation to 3D gravity via the AdS/CFT correspondence.

• We consider four-point functions with two heavy and two light external operators, along with the exchange of a light operator.
• By explicit computation, we establish precise agreement between these CFT objects and a simple picture of particle worldlines joined by cubic vertices propagating in asymptotically AdS$_3$ geometries (conical defects or BTZ black holes).
• We provide a simple argument that explains this agreement.