Renormalizable Theory Research Articles

CONFORMAL FIELD THEORY ON R × S3 FROM QUANTIZED GRAVITY

Conformal algebra on R × S3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess–Zumino action managing nonperturbative dynamics of the conformal factor in the metric field. It is shown that the residual diffeomorphism invariance in the radiation+ gauge is equal to the conformal symmetry, and the conformal transformation preserving the gauge-fixing condition that forms a closed algebra quantum mechanically is given by a combination of naive conformal transformation and a certain field-dependent gauge transformation. The unitarity issue of gravity is discussed in the context of conformal field theory. We construct physical states by solving the conformal invariance condition and calculate their scaling dimensions. It is shown that the conformal symmetry mixes the positive-metric and the negative-metric modes and thus the negative-metric mode does not appear independently as a gauge invariant state at all.

Nonanticommutative U(1) SYM theories: renormalization, fixed points and infrared stability

Renormalizable nonanticommutative SYM theories with chiral matter in the adjoint representation of the gauge group have been recently constructed in [arXiv: 0901.3094]. In the present paper we focus on the U(1) case with matter interacting through a cubic superpotential. For a single flavor, in a superspace setup and manifest background covariant approach we perform the complete one-loop renormalization and compute the beta-functions for all couplings appearing in the action. We then generalize the calculation to the case of SU(3) flavor matter with a cubic superpotential viewed as a nontrivial NAC generalization of the ordinary abelian N = 4 SYM and its marginal deformations. We find that, as in the ordinary commutative case, the NAC N = 4 theory is one-loop finite. We provide general arguments in support of all-loop finiteness. Instead, deforming the superpotential by marginal operators gives rise to beta-functions which are in general non-vanishing. We study the spectrum of fixed points and the RG flows. We find that nonanticommutativity always makes the fixed points unstable.

Determining the closed forms of the [formula omitted] anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra

Single scale quantities, as anomalous dimensions and hard scattering cross sections, in renormalizable Quantum Field Theories are found to obey difference equations of finite order in Mellin space. It is often easier to calculate fixed moments for these quantities compared to a direct attempt to derive them in terms of harmonic sums and their generalizations involving the Mellin parameter N. Starting from a sufficiently large number of given moments, we establish linear recurrence relations of lowest possible order with polynomial coefficients of usually high degree. Then these recurrence equations are solved in terms of d'Alembertian solutions where the involved nested sums are represented in optimal nested depth. Given this representation, it is then an easy task to express the result in terms of harmonic sums. In this process we compactify the result such that no algebraic relations occur among the sums involved. We demonstrate the method for the QCD unpolarized anomalous dimensions and massless Wilson coefficients to 3-loop order treating the contributions for individual color coefficients. For the most complicated subproblem 5114 moments were needed in order to produce a recurrence of order 35 whose coefficients have degrees up to 938. About four months of CPU time were needed to establish and solve the recurrences for the anomalous dimensions and Wilson coefficients on a 2 GHz machine requiring less than 10 GB of memory. No algorithm is known yet to provide such a high number of moments for 3-loop quantities. Yet the method presented shows that it is possible to establish and solve recurrences of rather large order and degree, occurring in physics problems, uniquely, fast and reliably with computer algebra.

Anisotropic cosmology and (super)stiff matter in Hořava’s gravity theory

We study anisotropic cosmology in Ho\ifmmode \check{r}\else \v{r}\fi{}ava's gravity theory and obtain Kasner-type solutions, valid for any number, $d$, of spatial dimensions. The corresponding exponents satisfy two relations, one involving the marginal coupling $\ensuremath{\lambda}$. Also, Ho\ifmmode \check{r}\else \v{r}\fi{}ava's (super)renormalizable theory predicts (super)stiff matter whose equation of state is $p=w\ensuremath{\rho}$, with $w\ensuremath{\ge}1$. We discuss briefly the implications of these results for the nature of cosmological collapse.

Enhanced spin fluctuations in the As-based filled skutteruditeLaFe4As12: AL139aNMR andA75sNQR study

We have grown single crystals of the itinerant-electron weak ferromagnet ${\text{LaFe}}_{4}{\text{As}}_{12}$ $({T}_{C}=3.8\text{ }\text{K})$ and refined its crystal structure parameters. We report experimental results of magnetic susceptibility and nuclear magnetic resonance at the La site and nuclear quadrupole resonance at the As site in the paramagnetic state for this compound. The temperature dependences of the static magnetic susceptibility, the $^{139}\text{L}\text{a}$ Knight shift, and the reciprocal of the product of the spin-lattice relaxation time and temperature $(1/{T}_{1}T)$ of both $^{139}\text{L}\text{a}$ and $^{75}\text{A}\text{s}$ nuclei can be consistently understood in terms of self-consistent renormalization theory of spin fluctuations for weak itinerant-electron ferromagnets.

Scale-invariant cosmological perturbations from Hořava-Lifshitz gravity without inflation

Based on the renormalizable theory of gravitation recently proposed by Hořava, we present a simple scenario to generate almost scale-invariant, super-horizon curvature perturbations. The anisotropic scaling with dynamical critical exponent z = 3 implies that the amplitude of quantum fluctuations of a free scalar field generated in the early epoch of the expanding universe is insensitive to the Hubble expansion rate and, thus, scale-invariant. Those fluctuations are later converted to curvature perturbations by the curvaton mechanism or/and the modulated decay of heavy particles/oscillating fields. This scenario works, for example, for power law expansion a∝t p with p>1/3 and, thus, does not require inflation. Also, this scenario does not rely on any additional assumptions such as the detailed balance condition.

Hořava–Lifshitz cosmology

The cosmological equations suggested by the non-relativistic renormalizable gravitational theory proposed by Hořava are considered. It is pointed out that the early universe cosmology has features that may give an alternative to inflation and the theory may be able to escape singularities.

Anomalous magnetization in the layered itinerant ferromagnet LaCoAsO

We synthesized weakly itinerant ferromagnet with layered structure LaCoAsO and measured the isothermal magnetizations at various temperatures. The isothermal magnetizations in a form of Arrott plot for weakly itinerant ferromagnets such as ${\text{ZrZn}}_{2}$, ${\text{Sc}}_{3}\text{In}$, ${\text{Ni}}_{3}\text{Al}$, and $\text{Y}{(\text{Co},\text{Al})}_{2}$ shows parallel linear relation over the wide temperature range near the Curie temperature ${T}_{\text{C}}$, while for LaCoAsO the square of the magnetization ${M}^{2}$ was found to show a convex curvature against $H/M$, similar to MnSi and ${\text{Fe}}_{x}{\text{Co}}_{1\ensuremath{-}x}\text{Si}$. We analyzed the magnetization of LaCoAsO at ${T}_{\text{C}}$ and estimated several parameters of spin fluctuations on the basis of self-consistent renormalization theory of spin fluctuations. We simulated a reciprocal magnetic susceptibility above ${T}_{\text{C}}$ and discussed the nature of spin fluctuations in LaCoAsO.

Chaotic period doubling

AbstractThe period doubling renormalization operator was introduced by Feigenbaum and by Coullet and Tresser in the 1970s to study the asymptotic small-scale geometry of the attractor of one-dimensional systems that are at the transition from simple to chaotic dynamics. This geometry turns out not to depend on the choice of the map under rather mild smoothness conditions. The existence of a unique renormalization fixed point that is also hyperbolic among generic smooth-enough maps plays a crucial role in the corresponding renormalization theory. The uniqueness and hyperbolicity of the renormalization fixed point were first shown in the holomorphic context, by means that generalize to other renormalization operators. It was then proved that, in the space ofC2+αunimodal maps, forα>0, the period doubling renormalization fixed point is hyperbolic as well. In this paper we study what happens when one approaches from below the minimal smoothness thresholds for the uniqueness and for the hyperbolicity of the period doubling renormalization generic fixed point. Indeed, our main result states that in the space ofC2unimodal maps the analytic fixed point is not hyperbolic and that the same remains true when adding enough smoothness to geta prioribounds. In this smoother class, calledC2+∣⋅∣, the failure of hyperbolicity is tamer than inC2. Things get much worse with just a bit less smoothness thanC2, as then even the uniqueness is lost and other asymptotic behavior becomes possible. We show that the period doubling renormalization operator acting on the space ofC1+Lipunimodal maps has infinite topological entropy.

Distribution functions in percolation problems

Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various such distribution functions in the limits where certain scaling variables become small or large. Our study includes the pair-connection probability, the distributions of the fractal masses of the backbone, the red bonds, and the shortest, the longest, and the average self-avoiding walk between any two points on a cluster, as well as the distribution of the total resistance in the random resistor network. Our analysis draws solely on general, structural features of the underlying diagrammatic perturbation theory, and hence our main results are valid to arbitrary loop order.

The Strongly Coupled Fourth Family and a First-Order Electroweak Phase Transition. I: -- Quark Sector --

In models of dynamical electroweak symmetry breaking due to strongly coupled fourth-family quarks and leptons, their low-energy effective descriptions may involve multiple composite Higgs fields, leading to a possibility that the electroweak phase transition at finite temperature is first order due to the Coleman-Weinberg mechanism. We examine the behavior of the electroweak phase transition based on the effective renormalizable Yukawa theory which consists of the fourth-family quarks and two SU(2)-doublet Higgs fields corresponding to the bilinear operators of the fourth-family quarks with/without imposing the compositeness condition. The strength of the first-order phase transition is estimated by using the finite-temperature effective potential at one-loop with the ring-improvement. In the Yukawa theory without the compositeness condition, it is found that there is a parameter region where the first-order phase transition is strong enough for the electroweak baryogenesis with the experimentally acceptable Higgs boson and fourth-family quark masses. On the other hand, when the compositeness condition is imposed, the phase transition turns out to be weakly first order, or possibly second order, although the result is rather sensitive to the details of the compositeness condition. Combining with the result of the Yukawa theory without the compositeness condition, it is argued that with the fourth-family quark masses in the range of 330-480 GeV, corresponding to the compositeness scale in the range of 1.0-2.3 TeV, the four-fermion interaction among the fourth-family quarks does not lead to the strongly first-order electroweak phase transition.

Renormalization in theories with modified dispersion relations: Weak gravitational fields

We consider a free quantum scalar field satisfying modified dispersion relations in curved spacetimes, within the framework of Einstein–Aether theory. Using a power counting analysis, we study the divergences in the adiabatic expansion of 〈ϕ2〉 and 〈Tμν〉, working in the weak field approximation. We show that for dispersion relations containing up to 2s powers of the spatial momentum, the subtraction necessary to renormalize these two quantities on general backgrounds depends on s in a qualitatively different way: while 〈ϕ2〉 becomes convergent for a sufficiently large value of s, the number of divergent terms in the adiabatic expansion of 〈Tμν〉 increases with s. This property was not apparent in previous results for spatially homogeneous backgrounds.

Superconductivity and Pseudogap in Quasi-Two-Dimensional Metals around the Antiferromagnetic Quantum Critical Point

Spin fluctuations (SF) and SF-mediated superconductivity (SC) in quasi-two-dimensional metals around the antiferrromagnetic (AF) quantum critical point (QCP) are investigated by using the self-consistent renormalization theory for SF and the strong coupling theory for SC. We introduce a parameter y0 as a measure for the distance from the AFQCP which is approximately proportional to (x-xc), x being the electron (e) or hole (h) doping concentration to the half-filled band and xc being the value at the AFQCP. We present phase diagrams in the T-y0 plane including contour maps of the AF correlation length and AF and SC transition temperatures TN and Tc, respectively. The Tc curve is dome-shaped with a maximum at around the AFQCP. The calculated one-electron spectral density shows a pseudogap in the high-density-of-states region near (pi,0) below around a certain temperature T* and gives a contour map at the Fermi energy reminiscent of the Fermi arc. These results are discussed in comparison with e- and h-doped high-Tc cuprates.

N=2, 4 supersymmetric gauge field theory in two-time physics

In the context of two-time physics in $4+2$ dimensions we construct the most general $N=2$, 4 supersymmetric Yang-Mills gauge theories for any gauge group G. This builds on our previous work for $N=1$ supersymmetry (SUSY). The action, the conserved SUSY currents, and the SU(N) covariant SUSY transformation laws are presented for both $N=2$ and $N=4$. When the equations of motion are used the SUSY transformations close to the supergroup $\mathrm{SU}(2,2|N)$ with $N=1$, 2, 4. The $\mathrm{SU}(2,2)=\mathrm{SO}(4,2)$ subsymmetry is realized linearly on $4+2$ dimensional flat spacetime. All fields, including vectors and spinors, are in $4+2$ dimensions. The extra gauge symmetries in 2T field theory, together with the kinematic constraints that follow from the action, remove all the ghosts to give a unitary theory. By choosing gauges and solving the kinematic equations, the 2T field theory in $4+2$ flat spacetime can be reduced to various shadows in various $3+1$ dimensional (generally curved) spacetimes. These shadows are related to each other by dualities. The conformal shadows of our theories in flat $3+1$ dimensions coincide with the well known counterpart $N=1$, 2, 4 supersymmetric massless renormalizable field theories in $3+1$ dimensions. It is expected that our more symmetric new structures in $4+2$ spacetime may be useful for nonperturbative or exact solutions of these theories.

Magnetic-field-induced crossover from non-Fermi to Fermi liquid at the quantum critical point ofYbCu5−xAux

The temperature $(T)$ dependence of the muon and $^{63}\text{C}\text{u}$ nuclear spin-lattice relaxation rates $1/{T}_{1}$ in ${\text{YbCu}}_{4.4}{\text{Au}}_{0.6}$ is reported over nearly four decades. It is shown that for $T\ensuremath{\rightarrow}0$ $1/{T}_{1}$ diverges following the behavior predicted by the self-consistent renormalization (SCR) theory for a ferromagnetic quantum critical point. On the other hand, the static uniform susceptibility ${\ensuremath{\chi}}_{s}$ is observed to diverge as ${T}^{\ensuremath{-}2/3}$ and $1/{T}_{1}T\ensuremath{\propto}{\ensuremath{\chi}}_{s}^{2}$, a behavior which is not accounted for by SCR theory. The application of a magnetic field $H$ is observed to induce a crossover to a Fermi-liquid behavior and for $T\ensuremath{\rightarrow}0$ $1/{T}_{1}$ is found to obey the scaling law $1/{T}_{1}(H)=1/{T}_{1}(0){[1+{({\ensuremath{\mu}}_{B}H/{k}_{B}T)}^{2}]}^{\ensuremath{-}1}$.

Electromagnetic and Scalar Pion form factor in the Kroll-Lee-Zumino model

The renormalizable Abelian quantum field theory model of Kroll, Lee, and Zumino is used at the one loop level to compute vertex corrections to the tree-level, Vector Meson Dominance (VMD) electromagnetic pion form factor. These corrections, together with the one-loop vacuum polarization contribution, imply a resulting electromagnetic pion form factor in excellent agreement with data in the whole range of accessible momentum transfers in the space-like region. The time-like form factor, which reproduces the Gounaris-Sakurai formula at and near the rho-meson peak, is unaffected by the vertex correction at order $\cal{O}$$(g^2)$. The KLZ model is also used to compute the scalar radius of the pion at the one loop level, finding $<r^{2}_{\pi}>_{S} = 0.40 fm^{2}$. This value implies for the low energy constant of chiral perturbation theory $\bar{l}_{4} =3.4$.

Realization of Symmetry in the ERG Approach to Quantum Field Theory

We review the use of the exact renormalization group for realization of symmetry in renormalizable field theories. The review consists of three parts. In part I (sects. 2,3,4), we start with the perturbative construction of a renormalizable field theory as a solution of the exact renormalization group (ERG) differential equation. We show how to characterize renormalizability by an appropriate asymptotic behavior of the solution for a large momentum cutoff. Renormalized parameters are introduced to control the asymptotic behavior. In part II (sects. 5--9), we introduce two formalisms to incorporate symmetry: one by imposing the Ward-Takahashi identity, and another by imposing the generalized Ward-Takahashi identity via sources that generate symmetry transformations. We apply the two formalisms to concrete models such as QED, YM theories, and the Wess-Zumino model in four dimensions, and the O(N) non-linear sigma model in two dimensions. We end this part with calculations of the abelian axial and chiral anomalies. In part III (sects. 10,11), we overview the Batalin-Vilkovisky formalism adapted to the Wilson action of a bare theory with a UV cutoff. We provide a few appendices to give details and extensions that can be omitted for the understanding of the main text. The last appendix is a quick summary for the reader's convenience.

Julius Erich Wess

Julius Erich Wess

On nonergodic property of Bose gas with weak pair interaction

In this paper we prove that Bose gas with weak pair interaction is non ergodic system. In order to prove this fact we consider the divergences in some nonequilibrium diagram technique. These divergences are analogous to the divergences in the kinetic equations discovered by Cohen and Dorfman. We develop the general theory of renormalization of such divergences and illustrate it with some simple examples. The fact that the system is non ergodic leads to the following consequence: to prove that the system tends to the thermal equilibrium we should take into account its behavior on its boundary. In this paper we illustrate this thesis with the Bogoliubov derivation of the kinetic equations.

Frustrated Magnetism in Vanadium Oxides

The effect of frustration in various localized and itinerant vanadium oxide compounds is discussed within next nearest neighbors Heisenberg and spin fluctuation models, respectively. In the localized moment case the S = 1/2 J1−J2-model on a square lattice exhibits a rich phase diagram with magnetic as well as exotic hidden order phases due to the interplay of frustration and quantum fluctuations. Their signatures in the high field magnetization and in magnetocaloric quantities are surveyed. The possible quantum phase transitions are discussed and applied to layered vanadium oxides of the type AA′VO(PO4)2 where A, A′ = Pb, Zn, Sr, Ba, Cd. In itinerant electron systems magnetic frustration may emerge as a result of electron correlations on a geometrically frustrated lattice. This mechanism causes enhanced spin fluctuations in a large region of momentum space and therefore can lead to a heavy fermion state at low temperatures as in the 3d spinel compound LiV2O4. The evidence from neutron scattering and NMR experiments is discussed within self-consistent renormalization theory based on local density approximation band structure calculations.