On the Shape Dependence of Entanglement Entropy

Understand

We study the shape dependence of entanglement entropy (EE) by deforming symmetric entangling surfaces.

• We show that entangling surfaces with a rotational or translational symmetry extremize (locally) the EE with respect to shape deformations that break some of the symmetry (i.e.
• the 1st order correction vanishes).
• This result applies to EE and Renyi entropy for any QFT in any dimension.