Entanglement Entropy of Two Spheres

We study the entanglement entropy S_{AB} of a massless free scalar field on two spheres A and B whose radii are R_1 and R_2, respectively, and the distance between the centers of them is r. The state of the massless free scalar field is the vacuum state. We obtain the result that the mutual information S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and proportional to the product of the areas of the two spheres when r>>R_1,R_2, where S_A and S_B are the entanglement entropy on the inside region of A and B, respectively. We discuss possible connections of this result with the physics of black holes.Comment: 17 pages, 9 figures; v4, added references, revised argument in section V, a typo in eq.(25) corrected, published versio

Holographic Studies of Entanglement Entropy in Superconductors

We present the results of our studies of the entanglement entropy of a superconducting system described holographically as a fully back-reacted gravity system, with a stable ground state. We use the holographic prescription for the entanglement entropy. We uncover the behavior of the entropy across the superconducting phase transition, showing the reorganization of the degrees of freedom of the system. We exhibit the behaviour of the entanglement entropy from the superconducting transition all the way down to the ground state at T=0. In some cases, we also observe a novel transition in the entanglement entropy at intermediate temperatures, resulting from the detection of an additional length scale.Comment: 21 pages, 14 figures. v2:Clarified some remarks concerning stability. v3: Updated to the version that appears in JHE

Entropy from AdS(3)/CFT(2)

We parametrize the (2+1)-dimensional AdS space and the BTZ black hole with Fefferman-Graham coordinates starting from the AdS boundary. We consider various boundary metrics: Rindler, static de Sitter and FRW. In each case, we compute the holographic stress-energy tensor of the dual CFT and confirm that it has the correct form, including the effects of the conformal anomaly. We find that the Fefferman-Graham parametrization also spans a second copy of the AdS space, including a second boundary. For the boundary metrics we consider, the Fefferman-Graham coordinates do not cover the whole AdS space. We propose that the length of the line delimiting the excluded region at a given time can be identified with the entropy of the dual CFT on a background determined by the boundary metric. For Rindler and de Sitter backgrounds our proposal reproduces the expected entropy. For a FRW background it produces a generalization of the Cardy formula that takes into account the vacuum energy related to the expansion.Comment: major revision with several clarifications and corrections, 22 page

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 Geometry of Entanglement Renormalization in Quantum Field Theories

We study a conjectured connection between the AdS/CFT and a real-space quantum renormalization group scheme, the multi-scale entanglement renormalization ansatz (MERA). By making a close contact with the holographic formula of the entanglement entropy, we propose a general definition of the metric in the MERA in the extra holographic direction, which is formulated purely in terms of quantum field theoretical data. Using the continuum version of the MERA (cMERA), we calculate this emergent holographic metric explicitly for free scalar boson and free fermions theories, and check that the metric so computed has the properties expected from AdS/CFT. We also discuss the cMERA in a time-dependent background induced by quantum quench and estimate its corresponding metric.Comment: 42pages, 9figures, reference added, minor chang

Entanglement Entropy for Singular Surfaces

We study entanglement entropy for regions with a singular boundary in higher dimensions using the AdS/CFT correspondence and find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge 'c'. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, similar universal terms may appear depending on the dimension and curvature of the singular locus.Comment: 66 pages,4 figures. Some typos are removed and a reference is adde

Holographic Entanglement Entropy in P-wave Superconductor Phase Transition

We investigate the behavior of entanglement entropy across the holographic p-wave superconductor phase transition in an Einstein-Yang-Mills theory with a negative cosmological constant. The holographic entanglement entropy is calculated for a strip geometry at AdS boundary. It is found that the entanglement entropy undergoes a dramatic change as we tune the ratio of the gravitational constant to the Yang-Mills coupling, and that the entanglement entropy does behave as the thermal entropy of the background black holes. That is, the entanglement entropy will show the feature of the second order or first order phase transition when the ratio is changed. It indicates that the entanglement entropy is a good probe to investigate the properties of the holographic phase transition.Comment: 19 pages,15 figures, extended discussion in Sec.5, references adde

On Shape Dependence and RG Flow of Entanglement Entropy

We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface has a conical or a wedge singularity. In (2+1)-dimensional field theory with a mass gap we calculate, for an arbitrary smooth entanglement contour, the expansion of the entropy in inverse odd powers of the mass. We show that the shape-dependent coefficients that arise are even powers of the extrinsic curvature and its derivatives. A useful dual construction of a (2+1)-dimensional theory, which allows us to exhibit these properties, is provided by the CGLP background. This smooth warped throat solution of 11-dimensional supergravity describes renormalization group flow from a conformal field theory in the UV to a gapped one in the IR. For this flow we calculate the recently introduced renormalized entanglement entropy and confirm that it is a monotonic function.Comment: 30 pages, 8 figures; v2 refs added, minor improvements; v3 minor improvements, JHEP versio

Identification and characterization of seed-specific transcription factors regulating anthocyanin biosynthesis in black rice

Black rice is rich in anthocyanin and is expected to have more healthful dietary potential than white rice. We assessed expression of anthocyanin in black rice cultivars using a newly designed 135 K Oryza sativa microarray. A total of 12,673 genes exhibited greater than 2.0-fold up- or down-regulation in comparisons between three rice cultivars and three seed developmental stages. The 137 transcription factor genes found to be associated with production of anthocyanin pigment were classified into 10 groups. In addition, 17 unknown and hypothetical genes were identified from comparisons between the rice cultivars. Finally, 15 out of the 17 candidate genes were verified by RT-PCR analysis. Among the genes, nine were up-regulated and six exhibited down-regulation. These genes likely play either a regulatory role in anthocyanin biosynthesis or are related to anthocyanin metabolism during flavonoid biosynthesis. While these genes require further validation, the results here underline the potential use of the new microarray and provide valuable insight into anthocyanin pigment production in rice

Interleukin-1β sequesters hypoxia inducible factor 2α to the primary cilium.

BACKGROUND: The primary cilium coordinates signalling in development, health and disease. Previously we have shown that the cilium is essential for the anabolic response to loading and the inflammatory response to interleukin-1β (IL-1β). We have also shown the primary cilium elongates in response to IL-1β exposure. Both anabolic phenotype and inflammatory pathology are proposed to be dependent on hypoxia-inducible factor 2 alpha (HIF-2α). The present study tests the hypothesis that an association exists between the primary cilium and HIFs in inflammatory signalling. RESULTS: Here we show, in articular chondrocytes, that IL-1β-induces primary cilia elongation with alterations to cilia trafficking of arl13b. This elongation is associated with a transient increase in HIF-2α expression and accumulation in the primary cilium. Prolyl hydroxylase inhibition results in primary cilia elongation also associated with accumulation of HIF-2α in the ciliary base and axoneme. This recruitment and the associated cilia elongation is not inhibited by blockade of HIFα transcription activity or rescue of basal HIF-2α expression. Hypomorphic mutation to intraflagellar transport protein IFT88 results in limited ciliogenesis. This is associated with increased HIF-2α expression and inhibited response to prolyl hydroxylase inhibition. CONCLUSIONS: These findings suggest that ciliary sequestration of HIF-2α provides negative regulation of HIF-2α expression and potentially activity. This study indicates, for the first time, that the primary cilium regulates HIF signalling during inflammation