Non-Linear Sigma Model and asymptotic freedom at the Lifshitz point

We construct the general O(N)-symmetric non-linear sigma model in 2+1 spacetime dimensions at the Lifshitz point with dynamical critical exponent z=2. For a particular choice of the free parameters, the model is asymptotically free with the beta function coinciding to the one for the conventional sigma model in 1+1 dimensions. In this case, the model admits also a simple description in terms of adjoint currents.Comment: 23 pages, 2 figure

Anti de Sitter 5D black hole solutions with a self-interacting bulk scalar field: a potential reconstruction approach

We construct asymptotically AdS black hole solutions, with a self-interacting bulk scalar field, in the context of 5D general relativity. As the observable universe is characterized by spatial flatness, we focus to solutions where the horizon of the black hole, and subsequently all 3D hypersurfaces for fixed radial coordinate,have zero spatial curvature. We examine two cases for the black hole scalar hair: a) an exponential decaying scalar field profile and b) an inverse power scalar field profile. The scalar black hole solutions we present in this paper, are characterized by four functions f(r), a(r), phi(r) and V(phi(r)). Only the functions phi(r) and a(r) are determined analytically, while the functions f(r) and V(phi(r)) are expressed semi-analytically, by integral formulas in terms of a(r). We present our numerical results in figures and we study in detail the characteristic properties of our solutions. We also note that the potential we obtain has a non-convex form in agreement with the corresponding "no hair theorem" for AdS space-times.Comment: 15 pages, 7 figure

Schwinger-Dyson approach for a Lifshitz-type Yukawa model

We consider a 3+1 dimensional field theory at a Lifshitz point for a dynamical critical exponent z=3, with a scalar and a fermion field coupled via a Yukawa interaction. Using the non-perturbative Schwinger-Dyson approach we calculate quantum corrections to the effective action. We demonstrate that a first order derivative kinetic term as well as a mass term for the fermion arise dynamically. This signals the restoration of Lorentz symmetry in the IR regime of the single fermion model, although for theories with more than one fermionic species such a conclusion will require fine-tuning of couplings. The limitations of the model and our approach are discussed.Comment: 20 pages, 2 figure

Black Holes in Ho\v{r}ava Gravity with Higher Derivative Magnetic Terms

We consider Horava gravity coupled to Maxwell and higher derivative magnetic terms. We construct static spherically symmetric black hole solutions in the low-energy approximation. We calculate the horizon locations and temperatures in the near-extremal limit, for asymptotically flat and (anti-)de Sitter spaces. We also construct a detailed balanced version of the theory, for which we find projectable and non-projectable, non-perturbative solutions.Comment: 17 pages. v2: Up to date with published version; some minor remarks and more reference

Geometrothermodynamics in Horava-Lifshitz gravity

We investigate the thermodynamic geometries of the most general static, spherically symmetric, topological black holes of the Ho\v{r}ava--Lifshitz gravity. In particular, we show that a Legendre invariant metric derived in the context of geometrothermodynamics for the equilibrium manifold reproduces correctly the phase transition structure of these black holes. Moreover, the limiting cases in which the mass, the entropy or the Hawking temperature vanish are also accompanied by curvature singularities which indicate the limit of applicability of the thermodynamics and the geometrothermodynamics of black holes. The Einstein limit and the case of a black hole with flat horizon are also investigated.Comment: Preliminary draf

Rationale, design and methodology for Intraventricular Pressure Gradients Study: a novel approach for ventricular filling assessment in normal and falling hearts

<p>Abstract</p> <p>Background</p> <p>Intraventricular pressure gradients have been described between the base and the apex of the left ventricle during early diastolic ventricular filling, as well as, their increase after systolic and diastolic function improvement. Although, systolic gradients have also been observed, data are lacking on their magnitude and modulation during cardiac dysfunction. Furthermore, we know that segmental dysfunction interferes with the normal sequence of regional contraction and might be expected to alter the physiological intraventricular pressure gradients. The study hypothesis is that systolic and diastolic gradients, a marker of normal left ventricular function, may be related to physiological asynchrony between basal and apical myocardial segments and they can be attenuated, lost entirely, or even reversed when ventricular filling/emptying is impaired by regional acute ischemia or severe aortic stenosis.</p> <p>Methods/Design</p> <p><it>Animal Studies: </it>Six rabbits will be completely instrumented to measuring apex to outflow-tract pressure gradient and apical and basal myocardial segments lengthening changes at basal, afterloaded and ischemic conditions. Afterload increase will be performed by abruptly narrowing or occluding the ascending aorta during the diastole and myocardial ischemia will be induced by left coronary artery ligation, after the first diagonal branch.</p> <p><it>Patient Studies: </it>Patients between 65-80 years old (n = 12), both genders, with severe aortic stenosis referred for aortic valve replacement will be selected as eligible subjects. A high-fidelity pressure-volume catheter will be positioned through the ascending aorta across the aortic valve to measure apical and outflow-tract pressure before and after aortic valve replacement with a bioprosthesis. Peak and average intraventricular pressure gradients will be recorded as apical minus outflow-tract pressure and calculated during all diastolic and systolic phases of cardiac cycle.</p> <p>Discussion</p> <p>We expect to validate the application of our method to obtain intraventricular pressure gradients in animals and patients and to promote a methodology to better understand the ventricular relaxation and filling and their correlation with systolic function.</p