Entanglement entropy across a deformed sphere

Abstract

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 arXiv:1407.7249 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, $C_T$. 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.

20 pages, 1 figure; v2: references added, typos fixed

References in corpus (15)

• Towards a derivation of holographic entanglement entropy
• Conformal collider physics: Energy and charge correlations
• Holographic c-theorems in arbitrary dimensions
• Entanglement entropy, conformal invariance and extrinsic geometry
• Thermodynamical Property of Entanglement Entropy for Excited States
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Entanglement Entropy: A Perturbative Calculation
• Universality in the geometric dependence of Renyi entropy
• Twist operators in higher dimensions
• Some results on the shape dependence of entanglement and Rényi entropies
• Exact and Numerical Results on Entanglement Entropy in (5+1)-Dimensional CFT
• On entanglement entropy functionals in higher derivative gravity theories
• Renyi entropy, stationarity, and entanglement of the conformal scalar
• Holographic stress tensor at finite coupling
• What surface maximizes entanglement entropy?

Cited by in corpus (11)

• Einsteinian cubic gravity
• Aspects of general higher-order gravities
• Comments on Squashed-sphere Partition Functions
• CFT correlators from shape deformations in Cubic Curvature Gravity
• Higher order gravities and the Strong Equivalence Principle
• Modular Hamiltonians for Euclidean Path Integral States
• More on Holographic Volumes, Entanglement, and Complexity
• Higher-Curvature Gravity, Black Holes and Holography
• Shape dependence of mutual information in the OPE limit: linear responses
• OPE of the stress tensors and surface operators
• Disks globally maximize the entanglement entropy in $2+1$ dimensions