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Diagonal Approximation for Holographic Rényi Entropies.

Geoff Penington1, Pratik Rath1

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This study derives a diagonal approximation for holographic Rényi entropy with multiple extremal surfaces. The findings refine the cosmic brane prescription, offering new insights into quantum information in holographic systems.

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Area of Science:

  • Quantum Gravity
  • Holographic Principle
  • Quantum Information Theory

Background:

  • The computation of Rényi entropy in holographic systems is crucial for understanding quantum information.
  • Existing methods, like the cosmic brane prescription, face challenges with multiple extremal surfaces.
  • The diagonal approximation offers a potential simplification for these computations.

Purpose of the Study:

  • To derive and validate the diagonal approximation for holographic Rényi entropy with two extremal surfaces.
  • To investigate the modified cosmic brane prescription for different values of alpha.
  • To compare the derived prescription with the original cosmic brane prescription.

Main Methods:

  • Derivation of the diagonal approximation for the case of two extremal surfaces.
  • Analysis of Rényi entropy computations up to O(logG) corrections.
  • Comparison of the modified and original cosmic brane prescriptions for alpha < 1 and alpha > 1.

Main Results:

  • The derived diagonal approximation accurately computes Rényi entropies up to O(logG) corrections.
  • For alpha < 1, a modified cosmic brane prescription is derived, differing from the original at leading order in G.
  • For alpha > 1, the original cosmic brane prescription is recovered without assuming unbroken replica symmetry.

Conclusions:

  • The diagonal approximation provides a robust method for calculating holographic Rényi entropy with multiple extremal surfaces.
  • The modified cosmic brane prescription offers a more accurate approach for certain parameter regimes.
  • This work advances the understanding of the interplay between gravity and quantum information in holographic contexts.