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2020

Modular Hamiltonians for Euclidean Path Integral States

Balakrishnan, Srivatsan, Parrikar, Onkar

Understand

We study half-space/Rindler modular Hamiltonians for excited states created by turning on sources for local operators in the Euclidean path integral in relativistic quantum field theories.

We derive a simple, manifestly Lorentzian formula for the modular Hamiltonian to all orders in perturbation theory in the sources.
We apply this formula to the case of shape-deformed half spaces in the vacuum state, and obtain the corresponding modular Hamiltonian to all orders in the shape deformation in terms of products of half-sided null energy operators, i.e., stress tensor components integrated along the future and past Rindler horizons.
In the special case where the shape deformation is purely null, our perturbation series can be resummed, and agrees precisely with the known formula for vacuum modular Hamiltonians for null cuts of the Rindler horizon.