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 AdS3 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 AdS3 kinematic space by the same quotient under which one obtains the defect from AdS3. 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.
Highlights
Invariant [11, 12]
In this paper we have shown that the kinematic space for a constant time slice of a static conical defect spacetime is a quotient of the kinematic space for time slices of pure AdS3
From the bulk our results were derived from the original differential entropy prescription, and by studying how the quotient acts on geodesics
Summary
We focus on static conical defect spacetimes and consider the kinematic space for a constant time slice. We show that the differential entropy approach [8], and the quotient approach [22] produce different fundamental regions of the same kinematic space, but are entirely equivalent
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