Aspects of holography in conical AdS3

Abstract

Abstract We study the Feynman propagator of free scalar fields in AdS3 with a conical defect. In the bulk, the defect is represented by a massive particle; in the dual CFT, it is a heavy operator that creates a highly excited state. We construct the propagator by solving the bulk equation of motion in the defect geometry, summing over the modes of the field, and passing to the boundary. The result agrees with a calculation based on the method of images in AdS3/ℤN, where it is also a sum over geodesic lengths. On the boundary, the propagator becomes a semiclassical heavy-light four-point function. We interpret the field modes as double-twist primary states formed by excitations of the scalar on top of the defect, and we check that the correlator is crossing-symmetric by matching its singular behavior to that of the semiclassical Virasoro vacuum block. We also argue that long-range correlations in conical AdS are “thermally” suppressed as the defect becomes more massive by studying the critical behavior of a continuous phase transition in the correlator at the BTZ threshold. Finally, we apply our results to holographic entanglement entropy by exploiting an analogy between free scalars and replica twist fields.