Kinematic space for conical defects

TL;DR

This paper explores the structure of kinematic space in conical defect spacetimes within AdS/CFT, revealing how non-minimal geodesics influence the space's definition and establishing a duality with boundary OPE blocks.

Contribution

It demonstrates how conical defect kinematic space can be derived from AdS$_3$ by quotienting and relates boundary OPE blocks to bulk geodesics, including non-minimal ones.

Findings

Conical defect kinematic space is a quotient of AdS$_3$ kinematic space.

Boundary OPE blocks can be decomposed into contributions from individual geodesics.

A duality between partial OPE blocks and bulk geodesic integrals is established.

Abstract

Kinematic space can be used as an intermediate step in the AdS/CFT dictionary and lends itself naturally to the description of diffeomorphism invariant quantities. From the bulk it has been defined as the space of boundary anchored geodesics, and from the boundary as the space of pairs of CFT points. When the bulk is not globally AdS$_3$ the appearance of non-minimal geodesics leads to ambiguities in these definitions. In this work conical defect spacetimes are considered as an example where non-minimal geodesics are common. From the bulk it is found that the conical defect kinematic space can be obtained from the AdS$_3$ kinematic space by the same quotient under which one obtains the defect from AdS$_3$. The resulting kinematic space is one of many equivalent fundamental regions. From the boundary the conical defect kinematic space can be determined by breaking up OPE blocks into contributions from individual bulk geodesics. A duality is established between partial OPE blocks and bulk fields integrated over individual geodesics, minimal or non-minimal.