Scale Invariant Theory Research Articles

Non-Static Plane Symmetric Zeldovich Fluid Model In ScaleInvariant Theory

We study the perfect fluid distribution in scale invariant theory ofgravitation, when the spacetime is described by non-static planesymmetric metric with a time-dependent gauge function. The Zeldovichmodel of the universe is constructed and some physical properties ofthe model are discussed.

SCALE SYMMETRY BREAKING FROM THE DYNAMICS OF MAXIMAL RANK GAUGE FIELD STRENGTHS

Scale invariant theories which contain maximal rank gauge field strengths (of D indices in D dimensions) are studied. The integration of the equations of motion of these gauge fields leads to the scale symmetry breaking of scale invariance. The cases in study are (i) the spontaneous generation of r-1 potentials in particle mechanics in a theory that contains only r-2 potentials in the scale invariant phase, (ii) mass generation in scalar field theories, (iii) generation of nontrivial dilaton potentials in generally covariant theories, and (iv) spontaneous generation of confining behavior in gauge theories. The possible origin of these models is discussed.

Scale-invariance in gravity and implications for the cosmological constant

Recently, a scale invariant theory was constructed by imposing a conformal symmetry on general relativity. The imposition of this symmetry changed the configuration space from superspace—the space of all Riemannian 3-metrics modulo diffeomorphisms—to conformal superspace—the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. However, despite numerous attractive features, the theory suffers from at least one major problem: the volume of the universe is no longer a dynamical variable. In attempting to resolve this problem a new theory is found which has several surprising and attractive features from both quantization and cosmological perspectives. Furthermore, it is an extremely restrictive theory and thus may provide testable predictions quickly and easily. One particularly interesting feature of the theory is the resolution of the cosmological constant problem.

Scaling solution, radion stabilization, and initial condition for brane-world cosmology

We propose a new, self-consistent and dynamical scenario which gives rise to well-defined initial conditions for five-dimensional brane-world cosmologies with radion stabilization. At high energies, the five-dimensional effective theory is assumed to have a scale invariance so that it admits an expanding scaling solution as a future attractor. The system automatically approaches the scaling solution and, hence, the initial condition for the subsequent low-energy brane cosmology is set by the scaling solution. At low energies, the scale invariance is broken and a radion stabilization mechanism drives the dynamics of the brane-world system. We present an exact, analytic scaling solution for a class of scale-invariant effective theories of five-dimensional brane-world models which includes the five-dimensional reduction of the Horava-Witten theory, and provide convincing evidence that the scaling solution is a future attractor.

Non-static plane symmetric cosmological model in Wesson’s theory

The problem of non-static plane symmetric perfect fluid distribution in Wesson’s [1] scale invariant theory of gravitation with a time-dependent gauge function is investigated. The false vacuum model of the universe is constructed and some physical properties of the model are discussed.

Letter: Static Plane Symmetric Cosmological Model in Wesson's Theory

The problem of static plane symmetric perfect fluid distribution in Wesson's scale invariant theory of gravitation with a time dependent gauge function is investigated. The cosmological model of the universe is constructed and some physical properties of the model are discussed.

A New Class of Conformal Field Theories with Anomalous Dimensions

The Wilsonian renormalization group (WRG) equation is used to derive a new class of scale invariant field theories with nonvanishing anomalous dimensions in 2-dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. When the coordinates of the target manifolds have nontrivial anomalous dimensions, vanishing of the $\beta$ function suggest the existence of novel conformal field theories whose target space is not Ricci flat. We construct such conformal field theories with ${\bf U}(N)$ symmetry. The theory has one free parameter a corresponding to the anomalous dimension of the scalar fields. The new conformal field theories are well behaved for positive a and have the central charge 3N, while they have curvature singularities at the boundary for a<0. When the target space is of complex 1-dimension, we obtain the explicit form of the Lagrangian, which reduces to two different kinds of free field theories in weak and in strong coupling limit. As a consistency test, the anomalous dimensions are reproduced in these two limits. The target space in this case looks like a semi-infinite cigar with one-dimension compactified to a circle.

Scale-invariant gravity: geometrodynamics

We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scale-invariant theories of gravity have been based on Weyl's idea of a compensating field, our direct approach dispenses with this and is built by extension of the method of best matching w.r.t. scaling developed in the parallel particle dynamics paper by one of the authors. In spatially compact GR, there is an infinity of degrees of freedom that describe the shape of 3-space which interact with a single volume degree of freedom. In conformal gravity, the shape degrees of freedom remain, but the volume is no longer a dynamical variable. Further theories and formulations related to GR and conformal gravity are presented. Conformal gravity is successfully coupled to scalars and the gauge fields of nature. It should describe the solar system observations as well as GR does, but its cosmology and quantization will be completely different.

Bianchi type I cosmological perfect fluid model in scale invariant theory

The intention of this paper is to study the perfect fluid distribution in scale invariant theory of gravity when the space-time is described by Bianchi type I metric with a time dependent gauge function. The cosmological equations for this space-time with gauge function are solved and some physical properties of the model are discussed.

SCALE INVARIANT THEORY FOR BIANCHI TYPE VIII AND IX SPACE-TIMES WITH PERFECT FLUID

In this paper we have taken an attempt to study the feasibility of scale invariant theory (Wesson, 1981a,b) in Bianchi type VIII and IX space-times with a time dependent gauge function (Dirac Gauge i.e. βα $$\tfrac{1}{t}$$ )and a matter field in the form of a perfect fluid. It is found that Bianchi type VIII (δ=1) space-time is feasible in this theory whereas Bianchi type IX (δ=-1) space-time is not feasible. In this feasible case a radiating model is constructed and its physical behaviour is discussed.

Bianchi Type V False Vacuum Cosmological Model in Scale-Invariant Theory

Intention of this paper is to study the perfect fluid distribution in scale-invariant theory of gravity when the space-time is described by Bianchi type V metric with a time-dependent gauge function (Dirac gauge). In this theory the false vacuum model of the universe is constructed and physical behaviors of the model is discussed.

Radial dimensional reduction: (anti) de Sitter theories from flat

We propose a new form of dimensional reduction that constrains dilatation instead of a component of momentum. It corresponds to replacing toroidal compactification in a Cartesian coordinate with that in the logarithm of the radius. Massive theories in de Sitter or anti de Sitter space are thus produced from massless (scale invariant) theories in one higher space or time dimension. As an example, we derive free massive actions for arbitrary representations of the (anti) de Sitter group in arbitrary dimensions. (Previous general results were restricted to symmetric tensors.) We also discuss generalizations to interacting theories.

Hierarchic trees with branching number close to one: Noiseless Kardar-Parisi-Zhang equation with additional linear term for imitating two-dimensional and three-dimensional phase transitions.

An imitation of two-dimensional (2D) field theory is formulated by means of a model on the hierarchic tree (with branching number close to one) with the same potential and the free correlators identical to 2D correlator ones. Such a model carries on some features of the original model for certain scale invariant theories. The renormalization group equation for the free energy is the noiseless Kardar-Parisi-Zhang equation with an additional linear term.

Bianchi Type VI1 Cosmological Model in Scale-Invariant Theory

In this paper, an attempt has been taken to study the perfect fluid distribution in the scale invariant theory of gravitation, when the space-time described by Bianchi type V metric with a time dependent gauge function. In this theory, a non-singular steady state model of the universe is constructed and some physical behaviors of the model are studied.

Incompatibility of Bianchi type III space time in scale invariant theory

It is shown here that the development of scale invariant theory of gravitation is not possible when (a) the space time is governed by diagonal Bianchi type III metric (b) the gauge function β depends on the time coordinate only (Dirac gauge) and (c) the energy momentum tensor is that of a perfect fluid.

Scale versus conformal invariance in the AdS/CFT correspondence

We present two examples of non-trivial field theories which are scale invariant, but not conformally invariant. This is done by placing certain field theories, which are conformally invariant in flat space, onto curved backgrounds of a specific type. We define this using the AdS/CFT correspondence, which relates the physics of gravity in asymptotically anti--de Sitter (AdS) spacetimes to that of a conformal field theory (CFT) in one dimension fewer. The AdS rotating (Kerr) black holes in five and seven dimensions provide us with the examples, since by the correspondence we are able to define and compute the action and stress tensor of four and six dimensional field theories residing on rotating Einstein universes, using the ``boundary counterterm'' method. The rotation breaks conformal but not scale invariance. The AdS/CFT framework is therefore a natural arena for generating such examples of non-trivial scale invariant theories which are not conformally invariant.

Comparing instanton contributions with exact results in N = 2 supersymmetric scale invariant theories

We discuss the general issues and ambiguities involved in matching the exact results for the low energy effective action of scale invariant N=2 supersymmetric QCD to those obtained by instanton methods. We resolve the reported disagreements and verify agreement between an infinite series of coefficients in the low energy effective actions calculated in the two approaches. In particular, we show that the exact low-energy effective couplings for SU(N) for all N with 2N fundamental hypermultiplets agree at a special vacuum on the Coulomb branch where a large unbroken discrete global symmetry makes the matching of parameters relatively straightforward.

New S-dualities in N = 2 supersymmetric SU(2) × SU(2) gauge theory

New S-dualities in a scale invariant N=2 gauge theory with SU(2) x SU(2) gauge group are derived from embeddings of the theory in two different larger asymptotically free theories. The true coupling space of the scale invariant theory is a 20-fold identification of the coupling space found in the M- and string-theory derivations of the low energy effective action, implying a larger S-duality group. Also, this coupling space is different from the naively expected direct product of two SL(2,Z) fundamental domains, as it contains a different topology of fixed points.

A scale-invariant model of statistical mechanics and modified forms of the first and the second laws of thermodynamics

A scale-invariant statistical theory of fields is presented that leads to invariant definition of density, velocity, temperature, and pressure. The definition of Boltzmann constant is introduced as k k = k = m k ν k c = 1.381 · 10 −23 J·K −1, suggesting that the Kelvin absolute temperature scale is equivalent to a length scale. Two new state variables called the reversible heat Q rev = TS and the reversible work W rev = PV are introduced. The modified forms of the first and second law of thermodynamics are presented. The microscopic definition of heat (work) is presented as the kinetic energy due to the random (peculiar) translational, rotational, and pulsational motions. The Gibbs free energy of an element at scale β is identified as the total system energy at scale (β − 1), thus leading to an invariant form of the first law of thermodynamics U β = Q β − W β + N eβ U β−1 .

Deriving N=2 S-dualities from scaling for product gauge groups

S-dualities in scale invariant N=2 supersymmetric field theories with product gauge groups are derived by embedding those theories in asymptotically free theories with higher rank gauge groups. S-duality transformations on the couplings of the scale invariant theory follow from the geometry of the embedding of the scale invariant theory in the Coulomb branch of the asymptotically free theory.