Two-point correlators of modular Hamiltonians obey entropy-like properties and equal the stress-tensor conformal block for spherical regions in CFT, including imaginary-time separations.
Equivalent Equations of Motion for Gravity and Entropy
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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.
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Correlation functions of von Neumann entropy
Two-point correlators of modular Hamiltonians obey entropy-like properties and equal the stress-tensor conformal block for spherical regions in CFT, including imaginary-time separations.