Superbalance of holographic entropy inequalities

The domain of allowed von Neumann entropies of a holographic field theory carves out a polyhedral cone — the holographic entropy cone — in entropy space. Such polyhedral cones are characterized by their extreme rays. For an arbitrary number of parties, it is known that the so-called perfect tensors are extreme rays. In this work, we constrain the form of the remaining extreme rays by showing that they correspond to geometries with vanishing mutual information between any two parties, ensuring the absence of Bell pair type entanglement between them. This is tantamount to proving that besides subadditivity, all non-redundant holographic entropy inequalities are superbalanced, i.e. not only do UV divergences cancel in the inequality itself (assuming smooth entangling surfaces), but also in the purification thereof

Acceleration-Induced Deconfinement Transitions in de Sitter Spacetime

In this note, we consider confining gauge theories in $D=2,3,4$ defined by $S^2$ or $T^2$ compactification of higher-dimensional conformal field theories with gravity duals. We investigate the behavior of these theories on de Sitter spacetime as a function of the Hubble parameter. We find that in each case, the de Sitter vacuum state of the field theory (defined by Euclidian continuation from a sphere) undergoes a deconfinement transition as the Hubble parameter is increased past a critical value. In each case, the corresponding critical de Sitter temperature is smaller than the corresponding Minkowski-space deconfinement temperature by a factor nearly equal to the dimension of the de Sitter spacetime. The behavior is qualitatively and quantitatively similar to that for confining theories defined by $S^1$ compactification of CFTs, studied recently in arXiv:1007.3996.Comment: 25 pages, 7 figure

Time evolution of entanglement entropy from a pulse

We calculate the time evolution of the entanglement entropy in a 1+1 CFT with a holographic dual when there is a localized left-moving packet of energy density. We find the gravity result agrees with a field theory result derived from the transformation properties of R\'enyi entropy. We are able to reproduce behavior which qualitatively agrees with CFT results of entanglement entropy of a system subjected to a local quench. In doing so we construct a finite diffeomorphism which tales three-dimensional anti-de Sitter space in the Poincar\'e patch to a general solution, generalizing the diffeomorphism that takes the Poincar\'e patch a BTZ black hole. We briefly discuss the calculation of correlation functions in these backgrounds and give results at large operator dimension.Comment: 18 pages, 6 figure

Extracting Spacetimes using the AdS/CFT Conjecture: Part II

Motivated by the holographic principle, within the context of the AdS/CFT Correspondence in the large t'Hooft limit, we investigate how the geometry of certain highly symmetric bulk spacetimes can be recovered given information of physical quantities in the dual boundary CFT. In particular, we use holographic entanglement entropy proposal (relating the entanglement entropy of certain subsystems on the boundary to the area of static minimal surfaces) to recover the bulk metric using higher dimensional minimal surface probes within a class of static, planar symmetric, asymptotically AdS spacetimes. We find analytic and perturbative expressions for the metric function in terms of the entanglement entropy of straight belt and circular disk subsystems of the boundary theory respectively. Finally, we discuss how such extractions can be generalised

Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure

We continue our study of the global properties of the z=2 Schroedinger space-time. In particular, we provide a codimension 2 isometric embedding which naturally gives rise to the previously introduced global coordinates. Furthermore, we study the causal structure by probing the space-time with point particles as well as with scalar fields. We show that, even though there is no global time function in the technical sense (Schroedinger space-time being non-distinguishing), the time coordinate of the global Schroedinger coordinate system is, in a precise way, the closest one can get to having such a time function. In spite of this and the corresponding strongly Galilean and almost pathological causal structure of this space-time, it is nevertheless possible to define a Hilbert space of normalisable scalar modes with a well-defined time-evolution. We also discuss how the Galilean causal structure is reflected and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.Comment: 32 page

Universal scaling properties of extremal cohesive holographic phases

We show that strongly-coupled, translation-invariant holographic IR phases at finite density can be classified according to the scaling behaviour of the metric, the electric potential and the electric flux introducing four critical exponents, independently of the details of the setup. Solutions fall into two classes, depending on whether they break relativistic symmetry or not. The critical exponents determine key properties of these phases, like thermodynamic stability, the (ir)relevant deformations around them, the low-frequency scaling of the optical conductivity and the nature of the spectrum for electric perturbations. We also study the scaling behaviour of the electric flux through bulk minimal surfaces using the Hartnoll-Radicevic order parameter, and characterize the deviation from the Ryu-Takayanagi prescription in terms of the critical exponents.Comment: v4: corrected a typo in eqn (3.29), now (3.28). Conclusions unchange

Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining

We argue that the entanglement entropy offers us a useful coarse-grained entropy in time-dependent AdS/CFT. We show that the total von-Neumann entropy remains vanishing even when a black hole is created in a gravity dual, being consistent with the fact that its corresponding CFT is described by a time-dependent pure state. We analytically calculate the time evolution of entanglement entropy for a free Dirac fermion on a circle following a quantum quench. This is interpreted as a toy holographic dual of black hole creations and annihilations. It is manifestly free from the black hole information problem.Comment: 25 pages, Latex, 8 figure