Causal diamonds in symmetric spacetimes obey a thermodynamic first law with negative temperature, and the Einstein equations can be recast as an entropy equilibrium condition, with a long-string CFT picture for non-AdS spaces.
Entanglement entropy from one-point functions in holographic states
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abstract
For holographic CFT states near the vacuum, entanglement entropies for spatial subsystems can be expressed perturbatively as an expansion in the one-point functions of local operators dual to light bulk fields. Using the connection between quantum Fisher information for CFT states and canonical energy for the dual spacetimes, we describe a general formula for this expansion up to second-order in the one-point functions, for an arbitrary ball-shaped region, extending the first-order result given by the entanglement first law. For two-dimensional CFTs, we use this to derive a completely explicit formula for the second-order contribution to the entanglement entropy from the stress tensor. We show that this stress tensor formula can be reproduced by a direct CFT calculation for states related to the vacuum by a local conformal transformation. This result can also be reproduced via the perturbative solution to a non-linear scalar wave equation on an auxiliary de Sitter spacetime, extending the first-order result in arXiv/1509.00113.
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Emergent Gravity in a Holographic Universe
Causal diamonds in symmetric spacetimes obey a thermodynamic first law with negative temperature, and the Einstein equations can be recast as an entropy equilibrium condition, with a long-string CFT picture for non-AdS spaces.