AdS geometry from CFT on a general conformally flat manifold

We construct an anti-de-Sitter (AdS) geometry from a conformal field theory (CFT) defined on a general conformally flat manifold via a flow equation associated with the curved manifold, which we refer to as the primary flow equation. We explicitly show that the induced metric associated with the primary flow equation becomes AdS whose boundary is the curved manifold. Interestingly, it turns out that such an AdS metric with conformally flat boundary is obtained from the usual Poincare AdS by a simple bulk diffeomorphism transformation. We also demonstrate that the emergence of such an AdS space is guaranteed only by the conformal symmetry at boundary, which converts to the AdS isometry after quantum averaging, as in the case of the flat boundary.Comment: 16 pages, no figur

Conserved charges in general relativity

We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved spacetime with Killing vectors. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of Schwarzschild and BTZ black holes by the volume integration of a delta function singularity. Employing the definition we also compute the total energy of a static compact star. It contains both the gravitational mass known as the Misner-Sharp mass in the Oppenheimer-Volkoff equation and the gravitational binding energy. We show that the gravitational binding energy has the negative contribution at maximum by 68% of the gravitational mass in the case of a constant density. We finally comment on a definition of generators associated with a vector field on a general curved manifold.Comment: 16 pages (single column), v3 (major revision): more discussion on a compact star included, a comparison with previous results given in the appendix, more references adde

Holographic geometry for non-relativistic systems emerging from generalized flow equations

An intriguing result presented by two of the present authors is that an anti de Sitter space can be derived from a conformal field theory by considering a flow equation. A natural expectation is that given a certain data on the boundary system, the associated geometry would be able to emerge from a flow, even beyond the conformal case. As a step along this line, we examine this scenario for non-relativistic systems with anisotropic scaling symmetries, such as Lifshitz field theories and Schr\"odinger invariant theories. In consequence we obtain a new hybrid geometry of Lifshitz and Schr\"odinger spacetimes as a general holographic geometry in this framework. We confirm that this geometry reduces to each of them by considering special non-relativistic models.Comment: 32 pages, no figure, v2: the definition of the metric operator changed, typos fixed, comments and references added, published versio

Clinical Application of Coagulation Biomarkers

Coagulopathy is of intense interest in the fields of emergency medicine, with many recent studies of coagulation biomarkers for clinical use. The occurrence of disseminated intravascular coagulation (DIC) also resulted in the activation of studies about the coagulopathy. At present DIC has been admitted in many clinical conditions and many coagulation biomarkers have been studied. Fibrin degradation product (FDP) and D-dimer are one type of coagulation biomarker. A characteristic of FDP and D-dimer is the rapid and dynamic elevation of their levels when fibrinolysis occurs in several acute diseases. In this chapter, we present the clinical application of FDP and D-dimer. In trauma, FDP and -dimer have been used for the evaluation of trauma severity, to predict the likelihood of hemorrhage and to evaluate the need for the transfusion of packed red blood cells. In cardiac pulmonary arrest (CPA), FDP and D-dimer have been useful for predicting the return of spontaneous circulation. Thus, the measurement of coagulation biomarkers is useful in the diagnosis and/or treatment of trauma and CPA

Charge Conservation, Entropy Current, and Gravitation

We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even without global symmetry. We also argue that the conserved current constructed from the (asymptotically) time-like vector field can be identified with the entropy current of the system. As a piece of evidence we show that the conserved charge defined therefrom satisfies the first law of thermodynamics for an isotropic system with a suitable definition of temperature. We apply our formulation to several gravitational systems such as the expanding universe, Schwarzschild and BTZ black holes, and gravitational plane waves. We confirm the conservation of the proposed entropy density under any homogeneous and isotropic expansion of the universe, the precise reproduction of the Bekenstein-Hawking entropy incorporating the first law of thermodynamics, and the existence of gravitational plane wave carrying no charge, respectively. We also comment on the energy conservation during gravitational collapse in simple models.Comment: 14 pages, 2 figures, published versio

Holographic computation of quantum corrections to the bulk cosmological constant

We explore the program of the construction of the dual bulk theory in the flow equation approach. We compute the vacuum expectation value of the Einstein operator at the next to leading order in the 1/n expansion using a free O(n) vector model. We interpret the next to leading correction as the quantum correction to the cosmological constant of the AdS space. We finally comment on how to generalize this computation to matrix elements of the Einstein operator for excited states.Comment: 1+16 pages, no figure, v2: minor corrections, v3: comments on one-loop tests of higher-spin/vector model duality and references added, typos fixed, published versio

What does a quantum black hole look like?

We take a first step towards a holographic description of a black hole by means of a flow equation. We consider a free theory of multiple scalar fields at finite temperature and study its holographic geometry defined through a free flow of the scalar fields. We find that the holographic metric has the following properties: i) It is an asymptotic Anti-de Sitter (AdS) black brane metric with some unknown matter contribution. ii) It has no coordinate singularity and milder curvature singularity. iii) Its time component decays exponentially at a certain AdS radial slice. We find that the matter spreads all over the space, which we speculate to be due to thermal excitation of infinitely many massless higher spin fields. We conjecture that the above three are generic features of a black hole holographically realized by the flow equation method.Comment: 15 pages, 4 figures. v2: 16 pages, 4 figures, comment on entropy and a reference added, a figure and discussion improved. v3: published version in PL

Conserved charges in general relativity

We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved space–time with Killing vectors. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of Schwarzschild and BTZ black holes by the volume integration of a delta function singularity. Employing the definition we also compute the total energy of a static compact star. It contains both the gravitational mass known as the Misner–Sharp mass in the Oppenheimer–Volkoff equation and the gravitational binding energy. We show that the gravitational binding energy has the negative contribution at maximum by 68% of the gravitational mass in the case of a constant density. We finally comment on a definition of generators associated with a vector field on a general curved manifold

Special flow equation and the GKP–Witten relation

We develop a framework for the reconstruction of the bulk theory dual to conformal field theory without any assumption by means of a flow equation. To this end we investigate a minimal extension of the free-flow equation and find that at a special parametrization the conformal transformation for a normalized smeared operator exactly becomes the isometry of anti-de Sitter space (AdS). By employing this special flow equation for O(N) vector models, we explicitly show that the AdS geometry as well as the scalar field satisfying the GKP–Witten relation concurrently emerge in this framework