Shape deformations of charged Rényi entropies from holography

by Stefano Baiguera (Ben-Gurion University)

Monday 20 Jun 2022, 14:45 → 15:30 Europe/Berlin

Charged and symmetry-resolved Rényi entropies are entanglement measures quantifying the degree of entanglement within different charge sectors of a theory with a conserved global charge. We use holography to determine the dependence of charged Rényi entropies on small shape deformations away from a spherical or planar entangling surface in general dimensions. This dependence is 
completely characterized by a single coefficient appearing in the two point function of the displacement operator associated with the Rényi defect. We extract this coefficient using its relation to the one 
point function of the stress tensor in the presence of a deformed 
entangling surface. This is mapped to a holographic calculation in the 
background of a deformed charged black hole with hyperbolic horizon. We obtain numerical solutions for different values of the chemical potential and replica number n in various spacetime dimensions, as well as analytic expressions for small chemical potential near n=1. When the Rényi defect becomes supersymmetric, we demonstrate  conjectured relation between the two point function of the displacement operator and the conformal weight of the twist operator.