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Diagonal Approximation for Holographic Rényi Entropies
Geoff Penington1, Pratik Rath1
1University of California, Berkeley, Center for Theoretical Physics and Department of Physics, California 94720, USA.
Physical Review Letters
|May 9, 2025
Summary
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.
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.
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