AdS/CFT prescription for angle-deficit space and winding geodesics

TL;DR

This paper computes boundary two-point correlators holographically in AdS$_3$ with a conical defect, comparing Green function and geodesic methods, revealing agreement for short correlations and discrepancies for long ones, especially in non-conformal cases.

Contribution

It provides a detailed holographic calculation of two-point correlators in AdS$_3$ with conical defects, clarifying the relation between Green functions and geodesic approximations.

Findings

Good agreement between methods for short correlators.

Discrepancies appear for long-range correlations.

Exact match in the $ ext{Z}_r$-orbifold case.

Abstract

We present the holographic computation of the boundary two-point correlator using the GKPW prescription for a scalar field in the AdS$_3$ space with a conical defect. Generally speaking, a conical defect breaks conformal invariance in the dual theory, however we calculate the classical Green functions for a scalar field in the bulk with conical defect and use them to compute the two-point correlator in the boundary theory. We compare the obtained general expression 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. Meanwhile, in case of $\mathbb{Z}_r$-orbifold, the GKPW result coincides with the one obtained via geodesic images prescription and with the general result for the boundary theory, which is conformal in this special case.