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Effective Density Matrix for Vacua in Asymptotically Flat Gravity.

Temple He1, Prahar Mitra2, Kathryn M Zurek1

  • 1California Institute of Technology, Walter Burke Institute for Theoretical Physics, Pasadena, California 91125, USA.

Physical Review Letters
|June 12, 2026
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Summary
This summary is machine-generated.

Researchers constructed the vacuum state density matrix for a large causal diamond in gravity. This work utilized the soft effective action to derive the modular Hamiltonian and its variance, revealing a relationship with the area and a UV cutoff.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • String Theory

Background:

  • The vacuum state in quantum field theory is fundamental.
  • Understanding the properties of quantum fields in curved spacetime is crucial.
  • Causal diamonds define regions of spacetime accessible to an observer.

Purpose of the Study:

  • To explicitly construct the density matrix for the vacuum state of a large spherically symmetric causal diamond in four-dimensional asymptotically flat gravity.
  • To extract the modular Hamiltonian associated with this vacuum state.
  • To compute the mean and variance of the modular Hamiltonian.

Main Methods:

  • Utilizing the soft effective action, which captures low-energy gravitational degrees of freedom.
  • Characterizing soft graviton and Goldstone modes from the Einstein-Hilbert action.
  • Integrating out the soft graviton mode to obtain an effective action for the Goldstone mode.

Main Results:

  • Explicit construction of the density matrix for the vacuum state.
  • Extraction of the modular Hamiltonian (K[over ^]_{s}) from the Goldstone mode effective action.
  • Calculation of the variance of the modular Hamiltonian as ⟨ΔK[over ^]_{s}^{2}⟩=A/ε_{UV}^{2}, where A is the area and ε_{UV} is a UV cutoff.

Conclusions:

  • The soft effective action provides a method to study vacuum state properties in gravitational systems.
  • The modular Hamiltonian and its properties are directly related to the geometry (area) and UV physics.
  • This work offers insights into the quantum structure of spacetime and entanglement in gravity.