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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ArXiv ePrint: 1604.05308
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Beach, M.J.S., Lee, J., Rabideau, C. et al. Entanglement entropy from one-point functions in holographic states. J. High Energ. Phys. 2016, 85 (2016). https://doi.org/10.1007/JHEP06(2016)085
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DOI: https://doi.org/10.1007/JHEP06(2016)085