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From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects
Kristan Jensen1, Andy O'Bannon2, Brandon Robinson2
1Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA.
Physical Review Letters
|July 20, 2019
Summary
This study explores conformal field theory (CFT) anomalies and entropy in 2D boundaries and defects. It finds that entanglement entropy relates to central charges, but no universal formula links them to thermal entropy.
Area of Science:
- Theoretical Physics
- High Energy Physics
- Quantum Field Theory
Background:
- Conformal field theories (CFTs) in two dimensions (2D) exhibit relations between Weyl anomaly, entanglement entropy (EE), and thermal entropy.
- These relations are investigated for 2D boundaries and defects in higher-dimensional CFTs (D≥3).
Purpose of the Study:
- To determine if established 2D CFT relations extend to 2D boundaries/defects in higher dimensions.
- To analyze the properties of central charges and entanglement entropy in these extended systems.
Main Methods:
- Analysis of the Weyl anomaly for 2D boundaries and defects, defining central charges (b and d₂).
- Investigation of entanglement entropy for a sphere centered on a planar defect.
- Holographic and free field calculations for specific supersymmetric CFTs.
Main Results:
- The central charge 'b' obeys a c-theorem for 2D boundaries/defects.
- A second central charge, 'd₂', interpreted as conformal dimension, is non-negative under the averaged null energy condition.
- Entanglement entropy of a sphere around a planar defect shows a logarithmic contribution fixed by 'b' and 'd₂'.
Conclusions:
- The study confirms extensions of 2D CFT relations to 2D boundaries/defects in higher dimensions.
- Calculated central charges for specific surface operators in 4D and 6D CFTs are consistent with the c-theorem.
- No universal Cardy-like formula connects central charges to thermal entropy in these systems.
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