On the RG running of the entanglement entropy of a circle

By H. Casini, M. Huerta. 2012

489 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f1a129edd2d03cb0c4677874288d4d04091f7731

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Citations in the corpus

Localization techniques in quantum field theories (2016, methodology): “12The same statement is true if we try to use the B-type topological twist [46].”
Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, methodology): “This relation has been used recently [19] to argue for (1.”
AdS description of induced higher-spin gauge theory (2013, background): “When s = 0 this is required by the F -theorem [11,69–72]—in fact, in that case δF must be positive when 3/2 < ∆ < 5/2.”
Bulk curves from boundary data in holography (2013, background): “ of these papers relates the c-theorem to strong subadditivity while the second relates strong subadditivity to general properties of geodesics in the bulk spacetime. Some relevant references include [47, 48, 49, 50]; see also [51] on the holographic emergence of Einstein’s equations. Eective Hamilt”
Central charges for BCFTs and holography (2012, methodology): “An analogue of c-theorem for three dimensional CFTs without boundaries has already been formulated in [29, 30, 31] and is called F-theorem.”
Entanglement entropy from a holographic viewpoint (2012, methodology): “Recently, an extension of this analysis has been obtained in three-dimensional field theories by applying the strong subadditivity to infinitely many subsystems in [32], which offers us an entropic proof of the so-called F-theorem [33].”
Interpolating between a and F (2014, background): “1 In the most physically interesting case d = 3, a proof of the F -theorem has been presented [14], relying on its exact relation with the entanglement entropy across a circle [15, 16].”
Mutual information and the F-theorem (2015, background): “J H E P 1 0 ( 2 0 1 5 ) 0 0 3 in [32], however, as it is a key element in the present proof, we elaborate on this point in appendix B.”
Entanglement entropy: Holography and renormalization group (2018, methodology): “There however are obstacles in the generalization to the higher dimensional cases which make the strong subadditivity inequalities be trivial due to logarithmic divergences coming from singular surfaces of intersecting boosted spheres (Casini and Huerta, 2012).”