Entanglement entropy for probe branes

Abstract

We give a prescription for calculating the entanglement entropy in holographic probe brane systems by systematically taking the leading order backreaction of the probe brane into account. We find a simple compact double integral formula, which is insensitive to many details of the backreaction, most notably the internal space or the non-metric fields sourced by the probe. We validate our method by comparing to exact results in solvable toy models. We also determine the entanglement entropies for a sphere and a strip in the top-down D3/D7 and D3/D5 system. For the sphere the entanglement entropy has also been obtained by other methods and we find perfect agreement.

Transport properties of spacetime-filling branes

“…The result of this calculation is shown in figure 3 for T b L 2 = 2 and T b L 2 = 0.1. The numeric result in this figure coincides, within numeric accuracy, with the prediction from hydrodynamics [35] 22) where the value is corrected by the volume of R 2 . The radial profile σ −1 (r) is used to obtain σ 0 (r) from (4.19).…”

“…From the point of view of the model, one obvious generalisation is to allow a finite codimension of the brane, in a similar way to the actions used in [22,23].…”

“…1 Whether the probe approximation is valid or not depends strongly on the kind of observables under consideration. In the absence of worldvolume gauge fields the perturbative solution to (1.1) is enough to calculate the entanglement entropy of probe branes [22,23].…”

Holographic entanglement entropy for massive flavours in dS 4

“…We conclude that the critical mass at the transition is m * l ≈ 1.32 in this example. The 11 Curiously the functional combination we see in Y1 also appears in the exact solution for the slipping mode in the supersymmetric version recently studied in [20,21]. In fact to linear order in m our solution agrees with their solution for the slipping mode.…”

“…For quantities calculated directly from the on-shell action, it is not necessary to go beyond the probe limit N f N c in which backreaction is neglected. This is not the case for flavour corrections to the EE, which are a topic of recent interest [10][11][12][13][14][15][16][17]. However, [13], building on [18], found a shortcut to the problem which does not require computing the backreaction.…”