Journal of High Energy Physics

, 2017:155 | Cite as

Kinematic space for conical defects

  • Jesse C. Cresswell
  • Amanda W. Peet
Open Access
Regular Article - Theoretical Physics


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.


AdS-CFT Correspondence Gauge-gravity correspondence Conformal Field Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Supplementary material

13130_2017_7131_MOESM1_ESM.cdf (39 kb)
ESM1 CD_Geodesics_Kinematic_Space.cdf (CDF 39 kb)
13130_2017_7131_MOESM2_ESM.nb (80 kb)
ESM2 CD_Geodesics_Kinematic_Space.nb (NB 80 kb)


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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of TorontoTorontoCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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