Equivalent Equations of Motion for Gravity and Entropy
  We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter pace. In doing so, we make use of the formalism of kinematic space [arXiv:1505.05515] and fields on this space, introduced in [arXiv:1604.03110]. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT. 
Bartlomiej Czech, Lampros Lamprou, Samuel McCandlish, Benjamin Mosk,   James Sully
hep-th