Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings

Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model (GN2), and its chiral cousin, the NJL2 model, have shown that there are phases with inhomogeneous crystalline condensates. These (static) condensates can be found analytically because the relevant Hartree-Fock and gap equations can be reduced to the nonlinear Schr\"odinger equation, whose deformations are governed by the mKdV and AKNS integrable hierarchies, respectively. Recently, Thies et al have shown that time-dependent Hartree-Fock solutions describing baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation, and can be mapped directly to classical string solutions in AdS3. Here we propose a geometric perspective for this result, based on the generalized Weierstrass spinor representation for the embedding of 2d surfaces into 3d spaces, which explains why these well-known integrable systems underlie these various Gross-Neveu gap equations, and why there should be a connection to classical string theory solutions. This geometric viewpoint may be useful for higher dimensional models, where the relevant integrable hierarchies include the Davey-Stewartson and Novikov-Veselov systems.Comment: 27 pages, 1 figur

The a-theorem and conformal symmetry breaking in holographic RG flows

We study holographic models describing an RG flow between two fixed points driven by a relevant scalar operator. We show how to introduce a spurion field to restore Weyl invariance and compute the anomalous contribution to the generating functional in even dimensional theories. We find that the coefficient of the anomalous term is proportional to the difference of the conformal anomalies of the UV and IR fixed points, as expected from anomaly matching arguments in field theory. For any even dimensions the coefficient is positive as implied by the holographic a-theorem. For flows corresponding to spontaneous breaking of conformal invariance, we also compute the two-point functions of the energy-momentum tensor and the scalar operator and identify the dilaton mode. Surprisingly we find that in the simplest models with just one scalar field there is no dilaton pole in the two-point function of the scalar operator but a stronger singularity. We discuss the possible implications.Comment: 50 pages. v2: minor changes, added references, extended discussion. v3: we have clarified some of the calculations and assumptions, results unchanged. v4: published version in JHE

All-mass n-gon integrals in n dimensions

We explore the correspondence between one-loop Feynman integrals and (hyperbolic) simplicial geometry to describe the "all-mass" case: integrals with generic external and internal masses. Specifically, we focus on $n$-particle integrals in exactly $n$ space-time dimensions, as these integrals have particularly nice geometric properties and respect a dual conformal symmetry. In four dimensions, we leverage this geometric connection to give a concise dilogarithmic expression for the all-mass box in terms of the Murakami-Yano formula. In five dimensions, we use a generalized Gauss-Bonnet theorem to derive a similar dilogarithmic expression for the all-mass pentagon. We also use the Schl\"afli formula to write down the symbol of these integrals for all $n$. Finally, we discuss how the geometry behind these formulas depends on space-time signature, and we gather together many results related to these integrals from the mathematics and physics literature.Comment: 49 pages, 8 figure

Schr\"odinger Holography with and without Hyperscaling Violation

We study the properties of the Schr\"odinger-type non-relativistic holography for general dynamical exponent z with and without hyperscaling violation exponent \theta. The scalar correlation function has a more general form due to general z as well as the presence of \theta, whose effects also modify the scaling dimension of the scalar operator. We propose a prescription for minimal surfaces of this "codimension 2 holography," and demonstrate the (d-1) dimensional area law for the entanglement entropy from (d+3) dimensional Schr\"odinger backgrounds. Surprisingly, the area law is violated for d+1 < z < d+2, even without hyperscaling violation, which interpolates between the logarithmic violation and extensive volume dependence of entanglement entropy. Similar violations are also found in the presence of the hyperscaling violation. Their dual field theories are expected to have novel phases for the parameter range, including Fermi surface. We also analyze string theory embeddings using non-relativistic branes.Comment: 62 pages and 6 figures, v2: several typos in section 5 corrected, references added, v3: typos corrected, references added, published versio

The role of copeptin as a diagnostic and prognostic biomarker for risk stratification in the emergency department

The hypothalamic-pituitary-adrenal axis is activated in response to stress. One of the activated hypothalamic hormones is arginine vasopressin, a hormone involved in hemodynamics and osmoregulation. Copeptin, the C-terminal part of the arginine vasopressin precursor peptide, is a sensitive and stable surrogate marker for arginine vasopressin release. Measurement of copeptin levels has been shown to be useful in a variety of clinical scenarios, particularly as a prognostic marker in patients with acute diseases such as lower respiratory tract infection, heart disease and stroke. The measurement of copeptin levels may provide crucial information for risk stratification in a variety of clinical situations. As such, the emergency department appears to be the ideal setting for its potential use. This review summarizes the recent progress towards determining the prognostic and diagnostic value of copeptin in the emergency department

Moduli Spaces of Cold Holographic Matter

We use holography to study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory with gauge group SU(Nc), in the large-Nc and large-coupling limits, coupled to a single massless (n+1)-dimensional hypermultiplet in the fundamental representation of SU(Nc), with n=3,2,1. In particular, we study zero-temperature states with a nonzero baryon number charge density, which we call holographic matter. We demonstrate that a moduli space of such states exists in these theories, specifically a Higgs branch parameterized by the expectation values of scalar operators bilinear in the hypermultiplet scalars. At a generic point on the Higgs branch, the R-symmetry and gauge group are spontaneously broken to subgroups. Our holographic calculation consists of introducing a single probe Dp-brane into AdS5 times S^5, with p=2n+1=7,5,3, introducing an electric flux of the Dp-brane worldvolume U(1) gauge field, and then obtaining explicit solutions for the worldvolume fields dual to the scalar operators that parameterize the Higgs branch. In all three cases, we can express these solutions as non-singular self-dual U(1) instantons in a four-dimensional space with a metric determined by the electric flux. We speculate on the possibility that the existence of Higgs branches may point the way to a counting of the microstates producing a nonzero entropy in holographic matter. Additionally, we speculate on the possible classification of zero-temperature, nonzero-density states described holographically by probe D-branes with worldvolume electric flux.Comment: 56 pages, 8 PDF images, 4 figure

Constraints on Nucleon Decay via "Invisible" Modes from the Sudbury Neutrino Observatory

Data from the Sudbury Neutrino Observatory have been used to constrain the lifetime for nucleon decay to ``invisible'' modes, such as n -> 3 nu. The analysis was based on a search for gamma-rays from the de-excitation of the residual nucleus that would result from the disappearance of either a proton or neutron from O16. A limit of tau_inv > 2 x 10^{29} years is obtained at 90% confidence for either neutron or proton decay modes. This is about an order of magnitude more stringent than previous constraints on invisible proton decay modes and 400 times more stringent than similar neutron modes.Comment: Update includes missing efficiency factor (limits change by factor of 2) Submitted to Physical Review Letter

Freeze-dried strawberry powder improves lipid profile and lipid peroxidation in women with metabolic syndrome: baseline and post intervention effects

<p>Abstract</p> <p>Background</p> <p>Strawberry flavonoids are potent antioxidants and anti-inflammatory agents that have been shown to reduce cardiovascular disease risk factors in prospective cohort studies. Effects of strawberry supplementation on metabolic risk factors have not been studied in obese populations. We tested the hypothesis that freeze-dried strawberry powder (FSP) will lower fasting lipids and biomarkers of oxidative stress and inflammation at four weeks compared to baseline. We also tested the tolerability and safety of FSP in subjects with metabolic syndrome. FSP is a concentrated source of polyphenolic flavonoids, fiber and phytosterols.</p> <p>Methods</p> <p>Females (n = 16) with 3 features of metabolic syndrome (waist circumference >35 inches, triglycerides > 150 mg/dL, fasting glucose > 100 mg/dL and < 126 mg/dL, HDL <50 mg/dL, or blood pressure >130/85 mm Hg) were enrolled in the study. Subjects consumed two cups of the strawberry drink daily for four weeks. Each cup had 25 g FSP blended in water. Fasting blood draws, anthropometrics, dietary analyses, and blood pressure measurements were done at baseline and 4 weeks. Biomarkers of oxidative stress and inflammation were measured using ELISA techniques. Plasma ellagic acid was measured using HPLC-UV techniques.</p> <p>Results</p> <p>Total cholesterol and LDL-cholesterol levels were significantly lower at 4 weeks versus baseline (-5% and -6%, respectively, p < 0.05), as was lipid peroxidation in the form of malondialdehyde and hydroxynonenal (-14%, p < 0.01). Oxidized-LDL showed a decreasing trend at 4 weeks (p = 0.123). No effects were noted on markers of inflammation including C-reactive protein and adiponectin. A significant number of subjects (13/16) showed an increase in plasma ellagic acid at four weeks versus baseline, while no significant differences were noted in dietary intakes at four weeks versus baseline. Thus, short-term supplementation of freeze-dried strawberries appeared to exert hypocholesterolemic effects and decrease lipid peroxidation in women with metabolic syndrome.</p