2017/08/31 by Nikola I. Gushterov, Andy O'Bannon, Andy O’Bannon +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal map #Cosmology and Gravitation Theories #Entropy (arrow of time) #Geometry #Lorentz covariance #Lorentz transformation #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Operator (biology) #Physics #Quantum #Quantum entanglement #Quantum mechanics #Renormalization group #Scalar field #Scaling #Spacetime #hep-th
paper · pdf · doi:10.1007/jhep10(2017)137
References clarified and updated compared to JHEP version
openalex publication_date 2017/10/01 · arxiv created 2017/10/27 · arxiv updated 2017/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We use holographic duality to study the entanglement entropy (EE) of Conformal Field Theories (CFTs) in various spacetime dimensions d, in the presence of various deformations: a relevant Lorentz scalar operator with constant source, a temperature T , a chemical potential μ, a marginal Lorentz scalar operator with source linear in a spatial coordinate, and a circle-compactified spatial direction. We consider EE between a strip or sphere sub-region and the rest of the system, and define the “entanglement density” (ED) as the change in EE due to the deformation, divided by the sub-region’s volume. Using the deformed CFTs above, we show how the ED’s dependence on the strip width or sphere radius, L, is useful for characterizing states of matter. For example, the ED’s small-L behavior is determined either by the dimension of the perturbing operator or by the first law of EE. For Lorentz-invariant renormalization group (RG) flows between CFTs, the “area theorem” states that the coefficient of the EE’s area law term must be larger in the UV than in the IR. In these cases the ED must therefore approach zero from below as L→∞. However, when Lorentz symmetry is broken and the IR fixed point has different scaling from the UV, we find that the ED often approaches the thermal entropy density from above, indicating area theorem violation.