Holographic dual of a conical defect

We consider a moving conical defect in the pure AdS$_3$ space–time and calculate two-point correlation functions of a corresponding two-dimensional boundary quantum field theory in the geodesic approximation. We show that the presence of the defect leads to a gravitational lensing of geodesics, and this results in a finite number of similar terms in the Green's function that correspond to winding geodesics in the bulk around the conical singularity. We show that for the quantized deficit angle $\gamma=\pi/2n$, the lensing produces domain wall excitations in the spectrum of the boundary theory.