Holographic entanglement plateaux

A puzzling aspect of the AdS/CFT correspondence is that a single bulk operator can be mapped to multiple different boundary operators, or precursors. By improving upon a recent model of Mintun, Polchinski, and Rosenhaus, we demonstrate explicitly how this ambiguity arises in a simple model of the field theory. In particular, we show how gauge invariance in the boundary theory manifests as a freedom in the smearing function used in the bulk-boundary mapping, and explicitly show how this freedom can be used to localize the precursor in different spatial regions. We also show how the ambiguity can be understood in terms of quantum error correction, by appealing to the entanglement present in the CFT. The concordance of these two approaches suggests that gauge invariance and entanglement in the boundary field theory are intimately connected to the reconstruction of local operators in the dual spacetime.

Section: Jhep04(2016)119mentioning

confidence: 99%

Precursors, gauge invariance, and quantum error correction in AdS/CFT

Freivogel

Jefferson

Kabir

2016

“…However, in this subsection we provide an algorithm that for any n enumerates the possible phases in a consistent manner, without omitting any solution or counting it twice, and which can easily be implemented (see the corresponding ancillary file). We do not assume a translation invariant spacetime, however we will assume a spacetime with simple topology, such as Poincaré AdS or a flat black brane, excluding possible phenomena such as entanglement plateaux [85], see also [83]. Our task then essentially boils down to finding the noncrossing partitions of a set with n elements, a well known combinatorial problem related to the Catalan numbers C n [86].…”

Section: The Phases Of the Union Of N Intervalsmentioning

confidence: 99%

“…However, the co-dimension one surface spanned between them and the boundary intervals would then become null or timelike at some point. As pointed out in [85], the co-dimension one surface required by the homology condition has to be restricted to be spacelike everywhere in the HRT prescription. Hence the configuration of figure 17 is also excluded in the dynamic case.…”

Section: The Phases Of the Union Of N Intervalsmentioning

confidence: 99%

Time evolution of entanglement for holographic steady state formation

Erdmenger

Fernández

Flory

et al. 2017

Within gauge/gravity duality, we consider the local quench-like time evolution obtained by joining two 1+1-dimensional heat baths at different temperatures at time t = 0. A steady state forms and expands in space. For the 2+1-dimensional gravity dual, we find that the "shockwaves" expanding the steady-state region are of spacelike nature in the bulk despite being null at the boundary. However, they do not transport information. Moreover, by adapting the time-dependent Hubeny-Rangamani-Takayanagi prescription, we holographically calculate the entanglement entropy and also the mutual information for different entangling regions. For general temperatures, we find that the entanglement entropy increase rate satisfies the same bound as in the 'entanglement tsunami' setups. For small temperatures of the two baths, we derive an analytical formula for the time dependence of the entanglement entropy. This replaces the entanglement tsunami-like behaviour seen for high temperatures. Finally, we check that strong subadditivity holds in this time-dependent system, as well as further more general entanglement inequalities for five or more regions recently derived for the static case.

“…We will not consider spacetimes which are asymptotically global AdS. In these cases the homology constraint in the holographic prescription (1.1) plays a crucial role [28,[86][87][88].…”

Section: Jhep12(2015)037mentioning

confidence: 99%

On shape dependence of holographic entanglement entropy in AdS4/CFT3

Fonda

Seminara

Tonni

2015

Self Cite

Abstract:We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS 4 , asymptotically AdS 4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS 4 , the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS 4 , the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence.