Aspects of Holography in Conical $AdS_3$

TL;DR

This paper investigates the behavior of scalar field propagators in conical $AdS_3$ spaces, exploring their properties, dual CFT interpretations, and implications for holographic entanglement entropy, revealing phase transitions related to defect mass.

Contribution

It provides a detailed analysis of scalar propagators in conical $AdS_3$, including mode solutions, boundary limits, and the effects of defects on correlations and entanglement entropy.

Findings

Propagator expressions sensitive to defect mass

Identification of a phase transition at the BTZ threshold

Suppression of long-range correlations with increasing defect mass

Abstract

We study the Feynman propagator of free scalar fields in $AdS_3$ with a conical defect. The propagator is built by solving the bulk equation of motion, summing over the modes of the field, and taking the boundary limit. We then perform several consistency checks. In the dual CFT, the operator responsible for the defect creates a highly excited state. We consider the exchange of the Virasoro identity block in the heavy-light limit to obtain an expression for the propagator sensitive to the mass of the defect. In $AdS_3/\mathbb{Z}_n$, we treat the propagator by the method of images and in the geodesic approximation. More generally, we argue that long-range correlations of the scalar are suppressed as the defect becomes more massive: we find a continuous phase transition in the correlator at the BTZ threshold and examine its critical behavior. Finally, we apply our results to holographic entanglement entropy using an analogy between our scalars and replica twist fields.