Renormalizable Theory Research Articles

Low-temperature electrical resistivity in paramagnetic spinelLiV2O4

The $3d$-electron spinel compound ${\text{LiV}}_{2}{\text{O}}_{4}$ exhibits heavy fermion behavior below 30 K which is related to antiferromagnetic spin fluctuations strongly enhanced in an extended region of momentum space. This mechanism explains enhanced thermodynamic quantities and nearly critical NMR relaxation in the framework of the self-consistent renormalization (SCR) theory. Here we show that the low-$T$ Fermi-liquid behavior of the resistivity and a deviation from this behavior for higher $T$ may also be understood within that context. We calculate the temperature dependence of the electrical resistivity $\ensuremath{\rho}(T)$ assuming that two basic mechanisms of the quasiparticle scattering, resulting from impurities and spin fluctuations, operate simultaneously at low temperature. The calculation is based on the variational principle in the form of a perturbative series expansion for $\ensuremath{\rho}(T)$. A peculiar behavior of $\ensuremath{\rho}(T)$ in ${\text{LiV}}_{2}{\text{O}}_{4}$ is related to properties of low-energy spin fluctuations whose $T$ dependence is obtained from SCR theory.

Geometry of the thermodynamics of the black holes in Hořava-Lifshitz gravity

Recently, a non-relativistic renormalizable theory of gravity has been proposed by Hořava. This theory is essentially a field theoretic model for a UV complete theory of gravity and it reduces to Einstein’s general relativity at large distances. Subsequently, Cai and his collaborators have obtained black hole solution in this gravity theory and studied the thermodynamic properties of the black hole solutions. In present work, we investigate the geometric thermodynamics of the above black hole solutions and examine the possibilities of any phase transition.

Emergent universe in Hor̆ava gravity

Recently Horava has proposed a non-relativistic renormalisable gravity theory with higher spatial derivatives in four dimensions which reduces to Einstein’s gravity at large distances with a non-vanishing cosmological constant but with improved UV behaviour. In this paper, we have considered the Friedman-Lemaitre-Robertson-Walker cosmological model in Horava gravity and the emergent scenario for all values of the spatial curvature k (=0,±1) has been studied. As a result, there are constraints on the parameters involved.

Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions

Theories defined in higher than four dimensions have been used in various frameworks and have a long and interesting history. Here we review certain attempts, developed over the last years, towards the construction of unified particle physics models in the context of higher-dimensional gauge theories with non-commutative extra dimensions. These ideas have been developed in two complementary ways, namely (i) starting with a higher-dimensional gauge theory and dimensionally reducing it to four dimensions over fuzzy internal spaces and (ii) starting with a four-dimensional, renormalizable gauge theory and dynamically generating fuzzy extra dimensions. We describe the above approaches and moreover we discuss the inclusion of fermions and the construction of realistic chiral theories in this context.

Renormalizable noncommutative quantum field theory

We discuss the Euclidean noncommutative \({\phi^4_4}\)-quantum field theory as an example of a renormalizable field theory. Using a Ward identity, Disertori, Gurau, Magnen and Rivasseau were able to prove the vanishing of the beta function for the coupling constant to all orders in perturbation theory. We extend this work and obtain from the Schwinger–Dyson equation a non-linear integral equation for the renormalised two-point function alone. The non-trivial renormalised four-point function fulfils a linear integral equation with the inhomogeneity determined by the two-point function. These integral equations might be the starting point of a nonperturbative construction of a Euclidean quantum field theory on a noncommutative space. We expect to learn about renormalisation from this almost solvable model.

Using line shapes to discriminate between binding mechanisms for theX(3872)

We construct line shapes for the X(3872) that generalize the Flatte and zero-range line shapes that have been considered previously. These line shapes are associated with scattering amplitudes that are exactly unitary for real values of the interaction parameters and can be derived from a renormalizable quantum field theory. The new line shapes can be used to discriminate between the alternative binding mechanisms in which the X(3872) is generated either dynamically by charm meson interactions or by a resonance near the D^{*0} Dbar^0 threshold. If the resonance is identified with the P-wave charmonium state chi'_{c1}, the interaction parameters can be constrained by using charmonium phenomenology. We analyze data on the X(3872) and also data from the Belle and Babar Collaborations on the invariant mass distribution of the charm mesons from the decay B -> K + D^{*0} Dbar^0 up to 4000 MeV. Our analysis is compatible with the mechanism for the X(3872) being either a fine-tuning of charm meson interactions or the fine-tuning of the chi'_{c1} to the D^{*0} Dbar^0 threshold. In particular, the data do not exclude a separate chi'_{c1} resonance between the D^{*+} D^- threshold and 4000 MeV.

HORAVA–LIFSHITZ GRAVITY, ABSOLUTE TIME, AND OBJECTIVE PARTICLES IN CURVED SPACE

Recently, Horava formulated a renormalizable theory of quantum gravity that reduces to general relativity at large distances but violates Lorentz invariance at small distances. The absolute time involved in this theory allows to define an objective notion of particles associated with quantization of fields in classical gravitational backgrounds. The Unruh effect and other observer-dependent notions of particles in curved space are interpreted as effects caused by interaction between the objective vacuum and the measuring apparatus made up of objective particles.

A proposal for covariant renormalizable field theory of gravity

The class of covariant gravity theories which have nice ultraviolet behavior and seem to be (super)-renormalizable is proposed. The apparent breaking of Lorentz invariance occurs due to the coupling with the effective fluid which is induced by Lagrange multiplier constrained scalar field. Spatially-flat FRW cosmology for such covariant field gravity may have accelerating solutions. Renormalizable versions of more complicated modified gravity which depends on Riemann and Ricci tensor squared may be constructed in the same way.

Horava–Lifshitz cosmology and quark–hadron phase transition

Recently, Horava proposed a non-relativistic renormalisable theory of gravitation which reduces to Einstein general relativity at large distances but violate Lorentz invariance at small distances. In this paper, we consider the quark–hadron phase transition in Horava–Lifshitz cosmology within an effective model of quantum chromodynamics. We study the evolution of the physical quantities relevant to the physical description of the early universe, namely, the energy density, temperature and the scale factor before, during, and after the phase transition and investigate the effects of the dynamical coupling constant λ and the 1/a4 term on the cosmological phase transition.

A renormalization fixed point for Lorenz maps

A Lorenz map is a Poincaré map for a three-dimensional Lorenz flow. We describe the theory of renormalization for Lorenz maps with a critical point and prove that a restriction of the renormalization operator acting on such maps has a hyperbolic fixed point. The proof is computer assisted and we include a detailed exposition on how to make rigorous estimates using a computer as well as the implementation of the estimates.

Renormalization versus strong form factors for one-boson-exchange potentials

We analyze the One Boson Exchange Potential from the point of view of Renormalization theory. We show that the nucleon-meson Lagrangean while predicting the NN force does not predict the NN scattering matrix nor the deuteron properties unambiguously due to the appearance of short distance singularities. While the problem has traditionally been circumvented by introducing vertex functions via phenomenological strong form factors, we propose to impose physical renormalization conditions on the scattering amplitude at low energies. Working in the large Nc approximation with pi,sigma,rho and omega mesons, we show that, once these conditions are applied, results for low energy phases of proton-neutron scattering as well as deuteron properties become largely insensitive to the form factors and to the vector mesons and yield a reasonable agreement with the data, for realistic values of the coupling constants.

On the consistency of the Horava Theory

With the goal of giving evidence for the theoretical consistency of the Hořava Theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Hořava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant λ. Since this constant breaks the general covariance under space-time diffeomorphisms, it is believed that arbitrary values of λ deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model. There have been a lot of interest about Hořava’s proposal of a new theory of gravity which in principle has a renormalizable quantum version [1] (an important part of the conceptual and technical basis was previously developed in Ref. [2]). To build such a theory, Hořava has proposed to abandon the principle of space-time relativity as a fundamental symmetry of nature, reducing the freedom to perform coordinate transformations to those transformations that preserve some preferred universal time-like foliation. The advantage of this scheme is that one can include higher spatial-derivative terms in the Lagrangian that render the theory renormalizable. According to Hořava’s point of view, jorgebellorin@usb.ve arestu@usb.ve

More on the renormalization of the horizon function of the Gribov–Zwanziger action and the Kugo–Ojima Green function(s)

In this paper we provide strong evidence that there is no ambiguity in the choice of the horizon function underlying the Gribov-Zwanziger action. We show that there is only one correct possibility which is determined by the requirement of multiplicative renormalizability. As a consequence, this means that relations derived from other horizon functions cannot be given a consistent interpretation in terms of a local and renormalizable quantum field theory. In addition, we also discuss that the Kugo-Ojima functions $u(p^2)$ and $w(p^2)$ can only be defined after renormalization of the underlying Green function(s).

Projectable Hořava–Lifshitz gravity in a nutshell

Approximately one year ago Hořava proposed a power-counting renormalizable theory of gravity which abandons local Lorentz invariance. The proposal has been received with growing interest and resulted in various different versions of Hořava-Lifshitz gravity theories, involving a colourful potpourri of new terminology. In this proceedings contribution we first motivate and briefly overview the various different approaches, clarifying their differences and similarities. We then focus on a model referred to as projectable Hořava–Lifshitz gravity and summarize the key results regarding its viability.

TIMELIKE GEODESIC MOTION IN HORAVA–LIFSHITZ SPACE–TIME

Recently a nonrelativistic renormalizable theory of gravitation has been proposed by P. Horava. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory is expected to flow to the relativistic value λ = 1, and could therefore serve as a possible candidate for a UV completion of Einstein's general relativity or an infrared modification thereof. In this paper under allowing the lapse function to depend on the spatial coordinates xias well as t, we obtain the spherically symmetric solutions. And then by analyzing the behavior of the effective potential for the particle, we investigate the timelike geodesic motion of particle in the Horava–Lifshitz space–time. We find that the nonradial particle falls from a finite distance to the center along the timelike geodesics when its energy is in an appropriate range. However, we find that it is complexity for radial particle along the timelike geodesics. There are three different cases due to the energy of radial particle: (i) when the energy of radial particle is higher than a critical value EC, the particle will fall directly from infinity to the singularity; (ii) when the energy of radial particle equals to the critical value EC, the particle orbit at r = rCis unstable, i.e. the particle will escape from r = rCto the infinity or to the singularity, depending on the initial conditions of the particle; (iii) when the energy of radial particle is in a proper range, the particle will rebound to the infinity or plunge to the singularity from a infinite distance, depending on the initial conditions of the particle.

F19NMR study of the coupling between4fand itinerant electrons in the pnictide superconductorsSmFeAsO1−xFx(0.15≤x≤0.2)

$^{19}$F NMR measurements in SmFeAsO$_{1-x}$F$_x$, for $0.15\leq x\leq 0.2$, are presented. The nuclear spin-lattice relaxation rate $1/T_1$ increases upon cooling with a trend analogous to the one already observed in CeCu$_{5.2}$Au$_{0.8}$, a quasi two-dimensional heavy-fermion intermetallic compound with an antiferromagnetic ground-state. In particular, the behaviour of the relaxation rate either in SmFeAsO$_{1-x}$F$_x$ or in CeCu$_{5.2}$Au$_{0.8}$ can be described in the framework of the self-consistent renormalization theory for weakly itinerant electron systems. Remarkably, no effect of the superconducting transition on $^{19}$F $1/T_1$ is detected, a phenomenon which can hardly be explained within a single band model.

Alternative boundary conditions for Monte Carlo simulations based on self-consistent correlations: Application to the two- and three-dimensional Ising models

An alternative to periodic boundary conditions is developed and tested in Monte Carlo simulations of the two- and three-dimensional Ising models. The boundary conditions are based on a mean-field approach that incorporates consistency constraints for the magnetization and correlations between nearest neighbors by means of an effective field and an extra coupling between nearest neighbors at the boundary of the simulation box. During the simulation the self-consistent equations are solved, and statistics are accumulated to obtain thermodynamic averages. In comparison with the standard periodic boundary conditions the method gives a more accurate estimation of nonuniversal magnitudes, such as the transition temperature and the behavior of the magnetization, but it cannot compete with the accuracy of other strategies such as finite-size scaling theory or Monte Carlo renormalization group to obtain critical exponents.

FRW universe in Hor̃ava gravity

Recently, a field theoretic model for a UV complete theory of gravity has been proposed by Ho\~{r}ava. This theory is a non-relativistic renormalizable gravity theory which coincides with Einstein's general relativity at large distances. Subsequently L\"{u} et al have formulated the modified Friedmann equations and have presented a solution in vacuum. In the present work, we rewrite the modified FRW equations in the form of usual FRW equations in Einstein gravity and consequences has been analyzed. Also the thermodynamics of the FRW universe has been studied.

Quantum field theory, gravity and cosmology in a fractal universe

We propose a model for a power-counting renormalizable field theory living in a fractal spacetime. The action is Lorentz covariant and equipped with a Stieltjes measure. The system flows, even in a classical sense, from an ultraviolet regime where spacetime has Hausdorff dimension 2 to an infrared limit coinciding with a standard $D$-dimensional field theory. We discuss the properties of a scalar field model at classical and quantum level. Classically, the field lives on a fractal which exchanges energy-momentum with the bulk of integer topological dimension D. Although an observer experiences dissipation, the total energy-momentum is conserved. The field spectrum is a continuum of massive modes. The gravitational sector and Einstein equations are discussed in detail, also on cosmological backgrounds. We find ultraviolet cosmological solutions and comment on their implications for the early universe.

On the renormalization of theories of a scalar chiral superfield

An exact renormalization group for theories of a scalar chiral superfield is formulated, directly in four dimensional Euclidean space. By constructing a projector which isolates the superpotential from the full Wilsonian effective action, it is shown that the nonperturbative nonrenormalization theorem follows, quite simply, from the flow equation. Next, it is argued that there do not exist any physically acceptable non-trivial fixed points. Finally, the Wess-Zumino model is considered, as a low energy effective theory. Following an evaluation of the one and two loop β-function coefficients, to illustrate the ease of use of the formalism, it is shown that the β-function in the massless case does not receive any nonperturbative power corrections.