Abstract
We study the holographic dual of the AdS3 spacetime with a conical defect. We calculate the boundary two-point correlator using the holographic Gubser-Klebanov-Polyakov/Witten dictionary for a scalar field in the bulk. We consider the general case, when the conical defect breaks conformal symmetry at the boundary. The results are compared with previous studies based on the geodesic approximation. They are in good agreement for short correlators, and main discrepancy comes in the region of long correlations. It is shown that in the case when the spacetime is the AdS3 /ℤN orbifold, both methods give the same result which also produces the result expected from the orbifold CFT.
Highlights
One of the key features of the AdS3/CFT2-correspondence [1, 2] is the fact that the 3D gravity is much simpler than its higher-dimensional counterparts, primarily because of its topological nature
The dynamics of the bulk objects described by these solutions is almost trivial in a sense that it can only be innately realized in the action of the identification Γ, or it can be induced by acting with isometries on the basic static configurations
Recent developments in techniques based on the extensive utilization of the Virasoro symmetry allow to study some properties of 3D gravity as quantum field theory [15, 16]
Summary
One of the key features of the AdS3/CFT2-correspondence [1, 2] is the fact that the 3D gravity is much simpler than its higher-dimensional counterparts, primarily because of its topological nature. The main object of study therein were two-point correlation functions and the entanglement entropy in the boundary dual to the AdS3-deficit spacetime in the framework of geodesic approximation. The goal of the present investigation is to study two-point boundary correlators in the framework of the holographic GKPW prescription [27, 28] on AdS3 with a conical defect, and clarify the applicability of the geodesic approximation in the AdS-deficit spacetime by comparison of GKPW correlators to the geodesic correlators obtained in the earlier work. In the general case we illustrate that the discontinuities in the geodesic result correspond to the non-conformal regime In this regime the most substantial discrepancy of two computations comes from the region of long-range correlations. Similar picture is observed in the time dependence of the correlators
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