Shape Deformations of Charged R\'enyi Entropies from Holography
- URL: http://arxiv.org/abs/2203.15028v2
- Date: Sat, 9 Jul 2022 10:03:34 GMT
- Title: Shape Deformations of Charged R\'enyi Entropies from Holography
- Authors: Stefano Baiguera, Lorenzo Bianchi, Shira Chapman and Dami\'an A.
Galante
- Abstract summary: We use holography to determine the dependence of charged R'enyi entropies on small shape deformations away from a spherical or planar entangling surface in general dimensions.
When the R'enyi defect becomes supersymmetric, we demonstrate a conjectured relation between the two point function of the displacement operator and the conformal weight of the twist operator.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Charged and symmetry-resolved R\'enyi 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 R\'enyi 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 R\'enyi 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 R\'enyi defect becomes supersymmetric, we demonstrate a conjectured
relation between the two point function of the displacement operator and the
conformal weight of the twist operator.
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