Kinematic space was originally defined in AdS3 as the space of geodesics. In this talk, I will generalize the concept of kinematic space to higher dimensions. Fields can be defined on this kinematic space, and these fields can be identified with "OPE blocks," contributions to the OPE from a single conformal family. In holographic theories, the OPE blocks are dual at leading order in 1/N to integrals of effective bulk fields along geodesics or homogeneous minimal surfaces in anti-de Sitter space. Thus, these operators pave the way for generalizing the Ryu-Takayanagi relation to other bulk fields. The dynamics of bulk fields are related to the dynamics of kinematic space fields via the intertwining property of integral transformations. In particular, the linearized gravitational equations are shown to be equivalent to a gauge-invariant wave equation on kinematic space.

References:
1) Equivalent Equations of Motion for Gravity and Entropy.
By Bartlomiej Czech, Lampros Lamprou, Samuel McCandlish, Benjamin Mosk, James Sully.
[arXiv:1608.06282 [hep-th]].
10.1007/JHEP02(2017)004.
JHEP 1702 (2017) 004.

2) Holographic equivalence between the first law of entanglement entropy and the linearized gravitational equations.
By Benjamin Mosk.
[arXiv:1608.06292 [hep-th]].
10.1103/PhysRevD.94.126001.
Phys.Rev. D94 (2016) no.12, 126001.

3) A Stereoscopic Look into the Bulk.
By Bartlomiej Czech, Lampros Lamprou, Samuel McCandlish, Benjamin Mosk, James Sully.
[arXiv:1604.03110 [hep-th]].
10.1007/JHEP07(2016)129.
JHEP 1607 (2016) 129.