Entanglement entropy across a deformed sphere

TL;DR

This paper demonstrates that in conformal field theories, the entanglement entropy across a deformed sphere is minimized by the sphere itself, with the quadratic deformation contribution being positive and governed by the stress tensor two-point function coefficient.

Contribution

The paper proves that the sphere minimizes the universal term in entanglement entropy among all shapes in CFTs, extending previous local extremum results to a global minimum, including higher curvature gravitational duals.

Findings

Sphere minimizes the universal entanglement entropy term.

Quadratic deformation contribution is positive and proportional to $C_T$.

Results hold for a wide class of CFTs with gravitational duals.

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.