Positivity, entanglement entropy, and minimal surfaces

The path integral representation for the Renyi entanglement entropies of integer index n implies these information measures define operator correlation functions in QFT. We analyze whether the limit $n\rightarrow 1$, corresponding to the entanglement entropy, can also be represented in terms of a path integral with insertions on the region's boundary, at first order in $n-1$. This conjecture has been used in the literature in several occasions, and specially in an attempt to prove the Ryu-Takayanagi holographic entanglement entropy formula. We show it leads to conditional positivity of the entropy correlation matrices, which is equivalent to an infinite series of polynomial inequalities for the entropies in QFT or the areas of minimal surfaces representing the entanglement entropy in the AdS-CFT context. We check these inequalities in several examples. No counterexample is found in the few known exact results for the entanglement entropy in QFT. The inequalities are also remarkable satisfied for several classes of minimal surfaces but we find counterexamples corresponding to more complicated geometries. We develop some analytic tools to test the inequalities, and as a byproduct, we show that positivity for the correlation functions is a local property when supplemented with analyticity. We also review general aspects of positivity for large N theories and Wilson loops in AdS-CFT.Comment: 36 pages, 10 figures. Changes in presentation and discussion of Wilson loops. Conclusions regarding entanglement entropy unchange

Holographic View on Quantum Correlations and Mutual Information between Disjoint Blocks of a Quantum Critical System

In (d+1) dimensional Multiscale Entanglement Renormalization Ansatz (MERA) networks, tensors are connected so as to reproduce the discrete, (d + 2) holographic geometry of Anti de Sitter space (AdSd+2) with the original system lying at the boundary. We analyze the MERA renormalization flow that arises when computing the quantum correlations between two disjoint blocks of a quantum critical system, to show that the structure of the causal cones characteristic of MERA, requires a transition between two different regimes attainable by changing the ratio between the size and the separation of the two disjoint blocks. We argue that this transition in the MERA causal developments of the blocks may be easily accounted by an AdSd+2 black hole geometry when the mutual information is computed using the Ryu-Takayanagi formula. As an explicit example, we use a BTZ AdS3 black hole to compute the MI and the quantum correlations between two disjoint intervals of a one dimensional boundary critical system. Our results for this low dimensional system not only show the existence of a phase transition emerging when the conformal four point ratio reaches a critical value but also provide an intuitive entropic argument accounting for the source of this instability. We discuss the robustness of this transition when finite temperature and finite size effects are taken into account.Comment: 21 pages, 5 figures. Abstract and Figure 1 has been modified. Minor modifications in Section 1 and Section

Corner contributions to holographic entanglement entropy

The entanglement entropy of three-dimensional conformal field theories contains a universal contribution coming from corners in the entangling surface. We study these contributions in a holographic framework and, in particular, we consider the effects of higher curvature interactions in the bulk gravity theory. We find that for all of our holographic models, the corner contribution is only modified by an overall factor but the functional dependence on the opening angle is not modified by the new gravitational interactions. We also compare the dependence of the corner term on the new gravitational couplings to that for a number of other physical quantities, and we show that the ratio of the corner contribution over the central charge appearing in the two-point function of the stress tensor is a universal function for all of the holographic theories studied here. Comparing this holographic result to the analogous functions for free CFT's, we find fairly good agreement across the full range of the opening angle. However, there is a precise match in the limit where the entangling surface becomes smooth, i.e., the angle approaches $\pi$, and we conjecture the corresponding ratio is a universal constant for all three-dimensional conformal field theories. In this paper, we expand on the holographic calculations in our previous letter arXiv:1505.04804, where this conjecture was first introduced.Comment: 62 pages, 6 figures, 1 table; v2: minor modifications to match published version, typos fixe

Higher Derivative Corrections to Holographic Entanglement Entropy for AdS Solitons

We investigate the behaviors of holographic entanglement entropy for AdS soliton geometries in the presence of higher derivative corrections. We calculate the leading higher derivative corrections for the AdS5 setup in type IIB string and for the AdS4,7 ones in M-theory. We also study the holographic entanglement entropy in Gauss-Bonnet gravity and study how the confinement/deconfinement phase transition observed in AdS solitons is affected by the higher derivative corrections.Comment: 1+25 pages, 12 figures, LaTeX; v2: footnotes and references adde

Towards a derivation of holographic entanglement entropy

We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry. Hence the conformal transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. The AdS/CFT dictionary allows us to calculate this thermodynamic entropy as the horizon entropy of a certain topological black hole. In even dimensions, we also demonstrate that the universal contribution to the entanglement entropy is given by A-type trace anomaly for any CFT, without reference to holography.Comment: 42 pages, 2 figures, few new ref's and comments adde

On shape dependence of holographic mutual information in AdS4

We study the holographic mutual information in AdS(4) of disjoint spatial domains in the boundary which are delimited by smooth closed curves. A numerical method which approximates a local minimum of the area functional through triangulated surfaces is employed. After some checks of the method against existing analytic results for the holographic entanglement entropy, we compute the holographic mutual information of equal domains delimited by ellipses, superellipses or the boundaries of two dimensional spherocylinders, finding also the corresponding transition curves along which the holographic mutual information vanishes

On shape dependence of holographic entanglement entropy in AdS4/CFT3

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 AdS4, asymptotically AdS4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS4, 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 AdS4, the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence

Characterization of highly frequent epitope-specific CD45RA(+)/CCR7(+/- )T lymphocyte responses against p53-binding domains of the human polyomavirus BK large tumor antigen in HLA-A*0201+ BKV-seropositive donors

Human polyomavirus BK (BKV) has been implicated in oncogenic transformation. Its ability to replicate is determined by the binding of its large tumor antigen (LTag) to products of tumor-suppressor genes regulating cell cycle, as specifically p53. We investigated CD8+ T immune responses to BKV LTag portions involved in p53 binding in HLA-A*0201+ BKV LTag experienced individuals. Peptides selected from either p53-binding region (LTag(351–450 )and LTag(533–626)) by current algorithms and capacity to bind HLA-A*0201 molecule were used to stimulate CD8+ T responses, as assessed by IFN-γ gene expression ex vivo and detected by cytotoxicity assays following in vitro culture. We observed epitope-specific immune responses in all HLA-A*0201+ BKV LTag experienced individuals tested. At least one epitope, LTag(579–587); LLLIWFRPV, was naturally processed in non professional antigen presenting cells and induced cytotoxic responses with CTL precursor frequencies in the order of 1/20'000. Antigen specific CD8+ T cells were only detectable in the CD45RA+ subset, in both CCR7+ and CCR7- subpopulations. These data indicate that widespread cellular immune responses against epitopes within BKV LTag-p53 binding regions exist and question their roles in immunosurveillance against tumors possibly associated with BKV infection

Inhibition of Endothelin-1-Mediated Contraction of Hepatic Stellate Cells by FXR Ligand

Activation of hepatic stellate cells (HSCs) plays an important role in the development of cirrhosis through the increased production of collagen and the enhanced contractile response to vasoactive mediators such as endothelin-1 (ET-1). The farnesoid X receptor (FXR) is a member of the nuclear receptor superfamily that is highly expressed in liver, kidneys, adrenals, and intestine. FXR is also expressed in HSCs and activation of FXR in HSCs is associated with significant decreases in collagen production. However, little is known about the roles of FXR in the regulation of contraction of HSCs. We report in this study that treatment of quiescent HSCs with GW4064, a synthetic FXR agonist, significantly inhibited the HSC transdifferentiation, which was associated with an inhibition of the upregulation of ET-1 expression. These GW4064-treated cells also showed reduced contractile response to ET-1 in comparison to HSCs without GW4064 treatment. We have further shown that GW4064 treatment inhibited the ET-1-mediated contraction in fully activated HSCs. To elucidate the potential mechanism we showed that GW4064 inhibited ET-1-mediated activation of Rho/ROCK pathway in activated HSCs. Our studies unveiled a new mechanism that might contribute to the anti-cirrhotic effects of FXR ligands