Comments on holographic entanglement entropy and RG flows

By R. Myers, A. Singh. Journal of High Energy Physics, 2012

207 citations recorded by the source corpus.

Using holographic entanglement entropy for strip geometry, we construct a candidate for a c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a ‘phase transition’ as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/18851dcbe2e15130220fef97c1c40eac1674b330

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Citations in the corpus

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 [43, 44, 45, 46]; see also [47] on the holographic emergence of Einstein’s equations. Eective Hamilt”
Entanglement entropy from a holographic viewpoint (2012, background): “See also [64, 65] for other relations between the entanglement entropy and RG flow.”
Islands in cosmology (2020, background): “The entropy of the narrow region C takes the form [49,50]”
Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, background): “) It has been proposed [7-11] that a similar inequality should hold in three dimensions,”
Extremal surfaces as bulk probes in AdS/CFT (2012, background): “in [37]; see also [48, 49] for more recent discussion).”
Mutual information and the F-theorem (2015, methodology): “The reader may find it easier to compare with the strip entropy in [35], which uses the same notation and conventions as in the present calculation.”
Entanglement entropy: Holography and renormalization group (2018, background): “…additional UV divergences whose coefficients depend on the opening angles (Bueno and Myers, 2015; Bueno et al., 2015; Casini and Huerta, 2007; Casini et al., 2009; Elvang and Hadjiantonis, 2015; Fradkin and Moore, 2006; Hirata and Takayanagi, 2007; Klebanov et al., 2012b; Myers and Singh, 2012b).”
On the RG running of the entanglement entropy of a circle (2012, background): “A related inequality was obtained in [27] for the strip geometry.”