Aspects of holography in conical \(\mathrm{AdS}_3\). (English) Zbl 07693917
Summary: We study the Feynman propagator of free scalar fields in \(\mathrm{AdS}_3\) 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 \(\mathrm{AdS}_3/\mathbb{Z}_N\), 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.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 83E05 | Geometrodynamics and the holographic principle |
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