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Universality of Rényi Entropy in Conformal Field Theory
Yuya Kusuki1,2,3, Hirosi Ooguri4,5, Sridip Pal4
1Kyushu University, Institute for Advanced Study, Fukuoka 819-0395, Japan.
Physical Review Letters
|August 27, 2025
Summary
We developed a thermal effective theory to calculate Rényi entropy in conformal field theories. This method provides a universal formula for entropy in the n→0 limit, applicable to spherical entangling surfaces.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- String Theory
Background:
- Rényi entropy quantifies entanglement in quantum systems.
- Understanding entanglement entropy is crucial for quantum field theories (QFTs).
- Previous studies lacked a universal formula for Rényi entropy in the n→0 limit for general QFTs.
Purpose of the Study:
- To derive a universal formula for the nth Rényi entropy (S_{A}^{(n)}) in the n→0 limit for conformal field theories (CFTs) in d dimensions.
- To investigate the behavior of entanglement entropy for spherical entangling surfaces with a UV cutoff.
- To explore the connection between entanglement entropy, density of states, and modular Hamiltonians.
Main Methods:
- Utilized the thermal effective theory to analyze the Rényi entropy.
- Applied the UV cutoff (ε) and considered spherical boundaries of the entanglement domain (A).
- Employed the hot spot idea in two dimensions for arbitrary positive n.
Main Results:
- Derived a universal formula for S_{A}^{(n)} in the n→0 limit: S_{A}^{(n)}=[f/(2πn)^{d-1}][Area(∂A)/(d-2)ε^{d-2}](1+O(n)).
- The theory dependence is captured by the cosmological constant (f) in the thermal effective action.
- Derived an analog of the Cardy formula for boundary operators in higher dimensions.
Conclusions:
- The thermal effective theory provides a powerful tool for calculating entanglement entropy in CFTs.
- The derived formula offers new insights into the structure of entanglement in quantum systems.
- The study clarifies the applicability of the hot spot idea and its differences across dimensions.
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