A conical deficit in the AdS4/CFT3 correspondence

TL;DR

This paper introduces a new duality within the AdS/CFT framework that enables the study of strongly coupled 2+1 dimensional field theories on conical spaces by deriving a conical AdS4 geometry and calculating related Green's functions.

Contribution

It proposes a novel duality connecting conical AdS4 geometries with 2+1 conical boundary spaces, facilitating analysis of strongly coupled theories in such geometries.

Findings

Derived a conical AdS4 spacetime solution with a static string and negative cosmological constant.

Calculated retarded Green's functions for scalar operators in the conical boundary space.

Established a correspondence between bulk conical geometries and boundary conical field theories.

Abstract

Inspired by the AdS/CFT correspondence we propose a new duality that allow the study of strongly coupled field theories living in a 2+1 conical space-time. Solving the 4-d Einstein equations in the presence of an infinite static string and negative cosmological constant we obtain a conical AdS4 space-time whose boundary is identified with the 2+1 cone found by Deser, Jackiw and 't Hooft. Using the AdS4/CFT3 correspondence we calculate retarded Green's functions of scalar operators living in the cone.