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Universal Feature of Charged Entanglement Entropy
Pablo Bueno1, Pablo A Cano2, Ángel Murcia3
1CERN, Theoretical Physics Department, CH-1211 Geneva 23, Switzerland.
Physical Review Letters
|July 22, 2022
Summary
Charged Rényi entropies generalize entanglement entropy using a chemical potential. For conformal field theories, the leading correction to entanglement entropy is quadratic in this potential, universally controlled by specific coefficients.
Area of Science:
- Quantum Field Theory
- Statistical Mechanics
- String Theory
Background:
- Rényi entropies generalize entanglement entropy and can be extended to include global symmetries.
- These 'charged Rényi entropies' depend on a chemical potential conjugate to the charge within the entangling region.
- For n=1, this yields a concept of charged entanglement entropy.
Purpose of the Study:
- To prove that the leading correction to uncharged entanglement entropy in general d(>=3)-dimensional conformal field theories (CFTs) is universally controlled.
- To establish the dependence of this correction on the chemical potential and specific CFT coefficients.
- To connect these findings with holographic calculations and properties of twist operators.
Main Methods:
- Derivation for general d-dimensional CFTs using universal identities related to twist operator magnetic response.
- Analytic holographic calculations in higher-curvature gravities and for free fields in d=4.
- Application of basic thermodynamic relations.
Main Results:
- The leading correction to entanglement entropy across a spherical surface in CFTs is quadratic in the chemical potential.
- This correction is positive definite and universally controlled by coefficients C_J and a_2.
- These coefficients characterize current correlators and energy flux.
Conclusions:
- The study provides a universal formula for the leading correction to entanglement entropy in CFTs.
- The results are consistent with holographic models and offer insights into quantum information in curved spacetimes.
- This work establishes a fundamental relationship between entanglement, symmetries, and gravitational phenomena in CFTs.
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