Improved image method for a holographic description of conical defects

The geodesics prescription in the holographic approach in the Lorentzian signature is applicable only for geodesics connecting spacelike-separated points at the boundary because there are no timelike geodesics that reach the boundary. Also, generally speaking, there is no direct analytic Euclidean continuation for a general background, such as a moving particle in the AdS space. We propose an improved geodesic image method for two-point Lorentzian correlators that is applicable for arbitrary time intervals when the space–time is deformed by point particles. We show that such a prescription agrees with the case where the analytic continuation exists and also with the previously used prescription for quasigeodesics. We also discuss some other applications of the improved image method: holographic entanglement entropy and multiple particles in the AdS$_3$ space.