On the RG running of the entanglement entropy of a circle

Details On the RG running of the entanglement entropy of a circle On the RG running of the entanglement entropy of a circle

2012-02-25

arxiv.org/abs/1202.5650v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 3 figures

Scientific paper

We show, using strong subadditivity and Lorentz covariance, that in three dimensional space-time the entanglement entropy of a circle is a concave function. This implies the decrease of the coefficient of the area term and the increase of the constant term in the entropy between the ultraviolet and infrared fixed points. This is in accordance with recent holographic c-theorems and with conjectures about the renormalization group flow of the partition function of a three sphere (F-theorem). The irreversibility of the renormalization group flow in three dimensions would follow from the argument provided there is an intrinsic definition for the constant term in the entropy at fixed points. We discuss the difficulties in generalizing this result for spheres in higher dimensions.

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