Spontaneous compactification in quantum Kaluza-Klein theories

We study the one-loop effective action for pure gravity in higher odd-dimensional spaces with a cosmological constant. We develop a method for computing the effective action for backgrounds which are a product of 4-dimensional space-time and an odd-dimensional sphere S^N. For N = 1 in harmonic gauge the potential has an unstable stationary point at which the one-loop corrected Newton constant has a wrong sign. For N > 1 in harmonic gauge there is an imaginary contribution to the effective potential from the Faddeev-Popov ghost. The results for spheres up to N = 17 are presented.     

Asymptotically de Sitter and anti-de Sitter black holes with confining electric potential

We study gravity interacting with a special kind of QCD-inspired nonlinear gauge field system which earlier was shown to yield confinement-type effective potential (the “Cornell potential”) between charged fermions (“quarks”) in flat space-time. We find new static spherically symmetric solutions generalizing the usual Reissner-Nordström-de Sitter and Reissner-Nordström-anti-de Sitter black holes with the following additional properties: (i) appearance of a constant radial electric field (in addition to the Coulomb one); (ii) novel mechanism of dynamical generation of cosmological constant through the non-Maxwell gauge field dynamics; (iii) appearance of confining-type effective potential in charged test particle dynamics in the above black hole backgrounds.     

The Z=Z(t/z)-Type Plane Wave Solutions of the Field Equations of General Relativity in a Plane Symmetric Space-Time

Taub (Ann. Math., 53:472?C490, 1951) has studied plane symmetry in Riemannian space-time by considering empty space-time admitting a three parameter group of motions. In this paper, we have deduced the line element of such a space-time for Z=Z(t/z)-type plane gravitational waves using suitable transformations following the concept of Takeno (Sci. Rep. Inst. Theor. Phys. Hiroshima Univ. 1, 1961), Lal and Ali (Tensor 20:281?C302, 1969). Furthermore it has been shown that the deduced space-time admit plane wave solutions of the field equations of general relativity containing electromagnetic terms. Also we have studied electromagnetic field except gauge transformation with particular cases with respect to ??.     

Symmetry breaking and restoration in Lifshitz type theories

We consider the one-loop effective potential at zero and finite temperature in scalar field theories with anisotropic space-time scaling. For z=2, there is a symmetry breaking term induced at one loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature. For z=3, we considered at first the case with a positive mass term at tree level and found no symmetry breaking effects induced at one loop, and then we study the case with a negative mass term at tree level where we cannot conclude about symmetry restoration effects at high temperature because of the imaginary parts that appear in the effective potential for small values of the scalar field.     

The heterotic sigma model in the presence of background gauge fields. Three-loop results

The covariant part of the β-functions for the heterotic σ-model in the presence of background gauge fields is calculated up to three-loop order. The equations β=0 are shown to coincide with the equations of motion derived from an effective space-time action. This effective action has been obtained previously via the string S-matrix approach.     

Vacuum Stability of the Wrong Sign (−ϕ 6) Scalar Field Theory

We apply the effective potential method to study the vacuum stability of the bounded from above (?? ⁶) (unstable) quantum field potential. The stability (?E/?b = 0) and the mass renormalization (? ² E/?b ² = M ²) conditions force the effective potential of this theory to be bounded from below (stable). Since bounded from below potentials are always associated with localized wave functions, the algorithm we use replaces the boundary condition applied to the wave functions in the complex contour method by two stability conditions on the effective potential obtained. To test the validity of our calculations, we show that our variational predictions can reproduce exactly the results in the literature for the \(\mathcal {PT}\) -symmetric ? ⁴ theory. We then extend the applications of the algorithm to the unstudied stability problem of the bounded from above (?? ⁶) scalar field theory where classical analysis prohibits the existence of a stable spectrum. Concerning this, we calculated the effective potential up to first order in the couplings in d space-time dimensions. We find that a Hermitian effective theory is instable while a non-Hermitian but \(\mathcal {PT}\) -symmetric effective theory characterized by a pure imaginary vacuum condensate is stable (bounded from below) which is against the classical predictions of the instability of the theory. We assert that the work presented here represents the first calculations that advocates the stability of the (?? ⁶) scalar potential.     

Topological invariants and the dynamics of an axial vector torsion field

A generalized theory of gravitation is discussed which is based on a Riemann-Cartan space-time,U ₄, with an axial vector torsion field. Besides Einstein's equations determining the metric of theU ₄, a system of nonlinear field equations is established coupling an axial vector source current to the axial vector torsion field. The properties of the solutions of these equations are discussed assuming a London-type condition relating the axial current and torsion field. To characterize the solutions use is made of the Euler and Pontrjagin forms and the associated quadratic curvature invariants for theU ₄ space-time. It is found that there exists for a Riemann-Cartan space-time a relation between the zeros of the axial vector torsion field and the singularities of the Pontrjagin invariant, which is analogous to the well-known Hopf relation between the zeros of vector fields and the Euler characteristic.     

Renormalization of Quantum Field Theory in Curved Space-Time and Renormalization Group Equations

The structure of quantum field theory renormalization in curved space-time is investigated. The equations allowing us to investigate the behaviour of vacuum energy and vertex functions in the limit of small distances in the external gravitational field are established. The behaviour of effective charges corresponding to the parameters of nonminimal coupling of the matter with the gravitational field is studied and the conditions under which asymptotically free theories become asymptotically conformally invariant are found. The examples of asymptotically conformally invariant theories are given. On the basis of a direct solution of renormalization group equations the effective potential in the external gravitational field and the effective action in the gravity with the high derivatives are obtained. The expression for the cosmological constant in terms of R²-gravity Lagrangian parameters is given which does not contradict the observable data. Renormalization and renormalization group equations for the theory in curved space-time with torsion are investigated.     

Scalars coupled to fermions in 1+1 dimensions

Using a method introduced in an earlier paper, we study a Bose field coupled to a Fermi field in 1+1 space-time dimensions. We employ the standard Hamiltonian formalism in which one computes the eigenvalues and eigenvectors of the Hamiltonian matrix. The matrix elements are computed using states defined on a lattice in momentum space. The results are compared with known strong and weak coupling limits. Bound states and renormalization effects are studied. We find that the choice of bare masses which give specified physical masses can be non-unique once a critical couplingλ _μ has been exceeded.     

Decoupling of long range interactions and temporally first cause: a toy model

Although the question of the unification of the gravitational and electromagnetic interactions has been obscured by the unification of the electromagnetic and nuclear interactions, SU(2) gravitational gauge degrees have been recently unified to the U(1) electromagnetic degrees. If the resulting tracks of charges which mediate the unifying Yang-Mills field are assumed to induce a (dilation) scale invariance on the space-time geometry, the decoupling of these long range interactions, which takes place via a U(1) symmetry (periodic time) break, could be related to the onset of an initial singularity and origin of (linear) time.     

The potential of effective field theory in NN scattering

We study an effective field theory of interacting nucleons at distances much greater than the pion's Compton wavelength. In this regime the NN potential is conjectured to be the sum of a delta function and its derivatives. The question we address is whether this sum can be consistently truncated at a given order in the derivative expansion, and systematically improved by going to higher orders. Regularizing the Lippmann-Schwinger equation using a cutoff we find that the cutoff can be taken to infinity only if the effective range is negative. A positive effective range — which occurs in nature — requires that the cutoff be kept finite and below the scale of the physics which has been integrated out, i.e. O(m_π). Comparison of cutoff schemes and dimensional regularization reveals that the physical scattering amplitude is sensitive to the choice of regulator. Moreover, we show that the presence of some regulator scale, a feature absent in dimensional regularization, is essential if the effective field theory of NN scattering is to be useful. We also show that one can define a procedure where finite cutoff dependence in the scattering amplitude is removed order by order in the effective potential. However, the characteristic momentum in the problem is given by the cutoff, and not by the external momentum. It follows that in the presence of a finite cutoff there is no small parameter in the effective potential, and consequently no systematic truncation of the derivative expansion can be made. We conclude that there is no effective field theory of NN scattering with nucleons alone.     

SU(2) gauge symmetry and anomaly of the S = 12 antiferromagnetic Heisenberg model in 2 + 1 dimensions

On the basis of the local SU (2) symmetry of the Heisenberg model, we show that the model, in a continuum limit, reduces to a problem of massless fermions coupled to an SU(2) gauge field in three space-time dimensions. The effective gauge field action changes by ± π ⦶ n ⦶ under a large gauge transformation with winding number n. To restore the gauge invariance, a parity- nonconserving, topological term is needed in the effective action. The physical implications are conjectured.     

Spinor Field Nonlinearity and Space-Time Geometry

Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI₀ type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI₀ type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time, though the isotropy of space-time can be attained for a large proportionality constant. As far as evolution is concerned, depending on the sign of coupling constant the model allows both accelerated and oscillatory mode of expansion. A negative coupling constant leads to an oscillatory mode of expansion, whereas a positive coupling constant generates expanding Universe with late time acceleration. Both deceleration parameter and EoS parameter in this case vary with time and are in agreement with modern concept of space-time evolution. In case of a Bianchi type-I space-time the non-diagonal components lead to three different possibilities. In case of a full BI space-time we find that the spinor field nonlinearity and the massive term vanish, hence the spinor field Lagrangian becomes massless and linear. In two other cases the space-time evolves into either LRSBI or FRW Universe. If we consider a locally rotationally symmetric BI(LRSBI) model, neither the mass term nor the spinor field nonlinearity vanishes. In this case depending on the sign of coupling constant we have either late time accelerated mode of expansion or oscillatory mode of evolution. In this case for an expanding Universe we have asymptotical isotropization. Finally, in case of a FRW model neither the mass term nor the spinor field nonlinearity vanishes. Like in LRSBI case we have either late time acceleration or cyclic mode of evolution. These findings allow us to conclude that the spinor field is very sensitive to the gravitational one.     

Charge,Geometry, and Effective Mass in the Kerr-Newman Solution to the Einstein Field Equations

It has been shown that for the Reissner-Nordström solution to the vacuum Einstein field equations charge, like mass, has a unique space-time signature (Marsh, Found. Phys. 38:293–300, 2008). The presence of charge results in a negative curvature. This work, which includes a discussion of effective mass, is extended here to the Kerr-Newman solution.     

A multidimensional global monopole and nonsingular cosmology

We consider a spherically symmetric global monopole in general relativity in (D=d+2)-dimensional space-time. For γ<d?1, where γ is a parameter characterizing the gravitational field strength, the monopole is shown to be asymptotically flat up to a solid angle defect. In the range d?1< γ<2d(d+1)/(d+2), the monopole space-time contains a cosmological horizon. Outside the horizon, the metric corresponds to a cosmological model of the Kantowski-Sachs type, where spatial sections have the topology ? × S ^d . In the important case where the horizon is far from the monopole core, the temporal evolution of the Kantowski-Sachs metric is described analytically. The Kantowski-Sachs space-time contains a subspace with a (d+1)-dimensional Friedmann-Robertson-Walker metric, whose possible cosmological application is discussed. Some estimates in the d=3 case show that this class of nonsingular cosmologies can be viable. In particular, the symmetry-breaking potential at late times can give rise to both dark matter and dark energy. Other results, generalizing those known in 4-dimensional space-time, are derived, in particular, the existence of a large class of singular solutions with multiple zeros of the Higgs field magnitude.     

The AdS5 Black Hole Space-time with the Perturbed?Dilaton Field Background

The AdS ₅ black hole space-time with perturbed dilaton field background considered. We use the holographic AdS/QCD soft-wall model to investigate the wave functions and the effective potential. In this model, glueballs are described by a massless scalar field in an AdS ₅ black hole with a dilaton soft-wall background. For the first time we use modified dilaton field and discuss the consequence of the perturbation. In order to obtain the effective potential we rewrite the equation of motion in the Schr?dinger like equation, then try to find corresponding solution.     

Quantum 3D spin-glass system on the scales of space-time periods of external electromagnetic fields

A dielectric medium consisting of rigidly polarized molecules has been treated as a quantum 3D disordered spin system. It is shown that using Birkhoff??s ergodic hypothesis the initial 3D disordered spin problem on scales of space-time periods of external field is reduced to two conditionally separable 1D problems. The first problem describes a 1D disordered N-particle quantum system with relaxation in random environment while the second one describes statistical properties of ensemble of disordered 1D steric spin chains of certain length. Basing on constructions which are developed in both problems, the coefficient of polarizability related to collective orientational effects under the influence of external field was calculated. On the basis of these investigations the equation of Clausius-Mossotti (CM) has been generalized as well as the equation for permittivity. It is shown that under the influence of weak standing electromagnetic fields in the equation of CM arising of catastrophe is possible, that can substantially change behavior of permittivity in the X-ray region on the macroscopic scale of space.     

M-theory on eight-manifolds

We show that in certain compactifications of M-theory on eight-manifolds to three-dimensional Minkowski space-time the four-form field strength can have a non-vanishing expectation value, while an N = 2 supersymmetry is preserved. For these compactifications a warp factor for the metric has to be taken into account. This warp factor is non-trivial in three space-time dimensions due to Chern-Simons corrections to the fivebrane Bianchi identity. While the original metric on the internal space is not Kahler, it can be conformally transformed to a metric that is Kähler and Ricci flat, so that the internal manifold has SU(4) holonomy.