Entanglement entropy, conformal invariance and extrinsic geometry

DOI10.1016/J.PHYSLETB.2008.05.071zbMATH Open1328.81209arXiv0802.3117OpenAlexW1970479743MaRDI QIDQ901724

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Publication date: 12 January 2016

Published in: (Search for Journal in Brave)

Abstract: We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface $Sigma$ that separates two subsystems of quantum strongly coupled $mathcalN=4$ SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal field theory. As a byproduct, we obtain a closed-form expression for the entanglement entropy in flat space-time when $Sigma$ is sphere $S_2$ and when $Sigma$ is two-dimensional cylinder. The contribution of the type A conformal anomaly to entanglement entropy is always determined by topology of surface $Sigma$ while the dependence of the entropy on the extrinsic geometry of $Sigma$ is due to the type B conformal anomaly.

Full work available at URL: https://arxiv.org/abs/0802.3117

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