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Local Modular Hamiltonians from the Quantum Null Energy Condition · Around

2017

Local Modular Hamiltonians from the Quantum Null Energy Condition

Koeller, Jason, Leichenauer, Stefan, Levine, Adam et al.

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The vacuum modular Hamiltonian $K$ of the Rindler wedge in any relativistic quantum field theory is given by the boost generator.

Here we investigate the modular Hamiltoninan for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane.
We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads $K" = T_{vv}$.
This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian.

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T. Faulkner, R. G. Leigh, O. Parrikar, and H. Wang, “Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition,” arXiv:1605.08072 [hep-th]

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