Shape dependence of entanglement entropy in conformal field theories

• DOI: 10.1007/jhep04(2016)088
• Publication Date: 2016-04-15T22:14:14Z
• Authors: Thomas Faulkner; Robert G. Leigh; Onkar Parrikar
• Keywords: Subadditivity

We study universal features in the shape dependence of entanglement entropy vacuum state a conformal field theory (CFT) on $\mathbb{R}^{1,d-1}$. consider across deformed planar or spherical entangling surface terms perturbative expansion infinitesimal deformation. In particular, we focus second order term this expansion, known as density. This quantity is to be non-positive by strong-subadditivity property. show from purely calculation that non-local part density any CFT universal, and proportional coefficient $C_T$ appearing two-point function stress tensors CFT. As applications our result, prove conjectured universality corner $\frac{\sigma}{C_T}=\frac{\pi^2}{24}$ $d=3$ CFTs, holographic Mezei formula for spheres.