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Holographic theories must satisfy boundary causality. We resolve a puzzle where bulk calculations seemingly violate this, showing how boundary conditions naturally fix the issue in the path integral.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • String Theory

Background:

  • Holographic theories relate boundary and bulk physics.
  • Boundary causality is a fundamental principle in quantum field theory.
  • Bulk calculations in holographic theories can present causal paradoxes.

Purpose of the Study:

  • To resolve the puzzle of apparent causality violation in holographic path integrals.
  • To demonstrate how boundary conditions reconcile bulk calculations with boundary causality.
  • To ensure the consistency of holographic principles.

Main Methods:

  • Analysis of the bulk Lorentzian path integral in holographic theories.
  • Careful treatment of boundary conditions within the holographic framework.
  • Investigating the behavior of commutators of boundary operators in the bulk.

Main Results:

  • The full bulk path integral includes metrics violating boundary causality.
  • A puzzle arises concerning vanishing commutators of space-like separated boundary operators.
  • The study shows how boundary conditions resolve this apparent contradiction.

Conclusions:

  • The bulk path integral, when properly treated with boundary conditions, naturally resolves causality puzzles in holography.
  • This work reinforces the consistency of holographic principles.
  • Understanding boundary conditions is crucial for reconciling bulk and boundary descriptions.