Shape Dependence of Entanglement Entropy in Conformal Field Theories
read the original abstract
We study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on $\mathbb{R}^{1,d-1}$. We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, and proportional to the coefficient $C_T$ appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient $\frac{\sigma}{C_T}=\frac{\pi^2}{24}$ in $d=3$ CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
When Symmetries Twist: Anomaly Inflow on Monodromy Defects
Monodromy defects for anomalous symmetries are defined as domain walls between symmetry generators and anomaly-induced topological orders, resulting in protected chiral edge modes and adiabatic pumping of gapless degr...
-
Curious QNEIs from QNEC: New Bounds on Null Energy in Quantum Field Theory
Derives new state-independent lower bounds on semi-local integrals of null energy flux in QFTs of two and higher dimensions using QNEC, strong subadditivity, and modular Hamiltonians.
-
Entropy Variations and Light Ray Operators from Replica Defects
Replica analysis shows QNEC saturation in interacting CFTs with twist gap because only the stress-tensor defect operator produces the contact term in the n to 1 limit.
-
Inhomogeneous Jacobi equation and Holographic subregion complexity
A variational perturbative method using the inhomogeneous Jacobi equation computes first-order changes in holographic subregion complexity for strip and disk subsystems under boosted black brane perturbations in AdS4,...
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.