Shape dependence of entanglement entropy in conformal field theories
By T. Faulkner, R. Leigh, Onkar Parrikar. Journal of High Energy Physics, 2015
137 citations recorded by the source corpus.
We study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on ℝ1,d−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathrm{\mathbb{R}}}^{1,d-1} $$\end{document}. 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 CT 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 σCT=π224\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{\sigma }{C_T}=\frac{\pi^2}{24} $$\end{document} in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.
Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/c96568faeb1dc5b52eca091263b02e17171ec92e
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Citations in the corpus
- Modular Hamiltonians on the null plane and the Markov property of the vacuum state (2017, background): “This property has been the subject of much of the recent interest and applications of modular Hamiltonians; see for example [1, 2, 3, 4, 5, 6, 7, 8, 9].”
- Modular Hamiltonians for deformed half-spaces and the averaged null energy condition (2016, methodology): “It is possible to perform the λ integral by going to the spectral representation (for details see [7, 12], where similar calculations were performed).”
- Entropy, extremality, euclidean variations, and the equations of motion (2017, background): “Then, we expect that the interacting graviton can be treated in the same way, by considering the interaction in entanglement perturbation theory [35, 43, 44].”