2014/11/30 by Márk Mezei · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cauchy stress tensor #Classical mechanics #Conformal field theory #Conformal map #Cosmology and Gravitation Theories #Curvature #Dual polyhedron #Entropy (arrow of time) #Geometry #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quadratic equation #Quantum entanglement #Quantum mechanics #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevd.91.045038
published as Phys. Rev. D 91, 045038 (2015) · 20 pages, 1 figure; v2: references added, typos fixed
arxiv created 2015/02/15 · openalex publication_date 2015/02/27 · arxiv updated 2015/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
I study the entanglement entropy (EE) across a deformed sphere in conformal field theories (CFTs). I show that the sphere (locally) minimizes the universal term in EE among all shapes. In the work of Allais and Mezei [Phys. Rev. D 91, 046002 (2015)] it was derived that the sphere is a local extremum, by showing that the contribution linear in the deformation parameter is absent. In this paper I demonstrate that the quadratic contribution is positive and is controlled by the coefficient of the stress tensor two-point function, CT. Such a minimization result contextualizes the fruitful relation between the EE of a sphere and the number of degrees of freedom in field theory. I work with CFTs with gravitational duals, where all higher curvature couplings are turned on. These couplings parametrize conformal structures in stress tensor n-point functions; hence I show the result for infinitely many CFT examples.