Instanton Type Research Articles

Supersymmetric Dirac-Born-Infeld axionic inflation and non-Gaussianity

An analysis is given of inflation based on a supersymmetric Dirac-Born-Infeld (DBI) action in an axionic landscape. The DBI model we discuss involves a landscape of chiral superfields with one U(1) shift symmetry which is broken by instanton type non-perturbative terms in the superpotential. Breaking of the shift symmetry leads to one pseudo-Nambu-Goldstone-boson which acts as the inflaton while the remaining normalized phases of the chiral fields generically labeled axions are invariant under the U(1) shift symmetry. The analysis is carried out in the vacuum with stabilized saxions, which are the magnitudes of the chiral fields. Regions of the parameter space where slow-roll inflation occurs are exhibited and the spectral indices as well as the ratio of the tensor to the scalar power spectrum are computed. An interesting aspect of supersymmetric DBI models analyzed is that in most of the parameter space tensor to scalar ratio and scalar spectral index are consistent with Planck data if slow roll occurs and is not eternal. Also interesting is that the ratio of the tensor to the scalar power spectrum can be large and can lie close to the experimental upper limit and thus testable in improved experiment. Non-Gaussianity in this class of models is explored.

Mass gap in Yang's theory of gravity

The quantization of a curvature-squared model of gravity, in the affine form proposed by Yang, is reconsidered in the path integral formulation. Due to its inherent Weyl invariance, sharing this with internal Yang–Mills fields, it or some of its topological generalizations are still a possible route to quantum gravity. Instanton type solutions with double duality properties exhibit a "vacuum degeneracy", i.e. a bifurcation into distinct classical Einsteinian backgrounds. For linearized fields, this conclusively induces a mass gap in the graviton spectrum, a feature which is an open problem in the quantization of internal Yang–Mills fields.

Relation between Lane–Emden solutions and radial solutions to the elliptic Heavenly equation on a disk

We provide a transformation between a type of solution to a Lane–Emden equation of second kind and a solution of the elliptic Heavenly equation on a disk. By doing so, we show that any solution of this Lane–Emden equation of second kind corresponds to an infinite family of solutions to the Heavenly equation. This Lane–Emden equation is naturally formulated as a boundary value problem, which makes it somewhat distinct from the initial value problem versions in the literature. We obtain simple analytical solutions of this Lane–Emden equation and associated boundary value problem, and then we use these analytical solutions to construct a family of solutions for the elliptic Heavenly equation. The obtained solutions are radial solutions to the Heavenly equation; that is, they exhibit radial symmetry. In effect, we obtain a relation between radially-symmetric self-dual gravitational instantons and the Lane–Emden approximation to the structure of a neutron star. In other words, the radially symmetric neutron star under the Lane–Emden model can be seen as a special type of gravitational instanton.

Explicit Solutions of Maxwell-Einstein Equations

This article concerns the effect of gravitation field of the spherical electro-magnetic wave (EMW) on its propagation in vacuum. For this it was received a solution of the coupled Maxwell-Einstein equations. It is shown that in addition with traveling wave EMW at а great distance some new solution of so-called instanton type exists. It describes the process of quantum tunneling between degenerate states corresponding to convergent and divergent spherical waves in quasi-classical approximation. It is shown that these solutions for zero moment momentum describe fields of point-like charges - electric e and magnetic g. Symmetry of Maxwell equations with respect to group U(1) of dual transformations: (E+iH) → (E+iH)e iα , (E and H are electric and magnetic fields, α - is real parameter) is valid for generalized charge e + ig, which is transformed in the same manner. Spontaneous breaking of symmetry of this group, which is characterized tgα = - g/e, leads to arising mass-less particles (photons?) due to Goldstone theorem. This also leads to the fact that magnetic charges cannot be detected in Nature.

Publisher’s Note: Einsteinian gravity from BRST quantization of a topological action [Phys. Rev. D77, 084020 (2008)

The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a `vacuum degeneracy'. By modifying the duality via a scale breaking term, we demonstrate that only Einstein's equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of `dark energy' as well as `dark matter' modeled by a torsion induced quintaxion.

Einsteinian gravity from BRST quantization of a topological action

In order to deduce Einsteinian gravity from a topological action, we start from the metric-free Pontrjagin invariant in four dimensions. Using the Becchi-Rouet-Stora-Tyutin antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature. They correspond to classical instanton type solutions of a curvature-squared model of gravity, in the affine form proposed already by Weyl and Yang. However, the exact vacuum solutions with double duality properties exhibit a ``vacuum degeneracy.'' By modifying the duality of the curvature via scale breaking terms, we demonstrate that only Einstein's equations with an induced cosmological constant of partially topological origin emerge for the macroscopic ``background.''

The generalized Fubini instanton

We show that ( 1 + 2 ) nonlinear Klein–Gordon equation with negative coupling admits an exact solution which appears to be the linear superposition of the plane wave and the nonsingular rational soliton. We show that the same approach allows to construct the solution of similar properties for the Euclidean ϕ 4 model with broken symmetry. Interestingly, this regular solution will be of instanton type only in the D ⩽ 5 Euclidean space. Thus one can use the generalized Fubini instantons (in quantum cosmology for example) only for the case of the single infinite extra dimension.

Einsteinian gravity from a topological action

The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a ‘vacuum degeneracy’. By modifying the duality via a scale breaking term, we demonstrate that only Einstein’s equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of ‘dark energy’ as well as ‘dark matter’ modeled by a torsion induced quintaxion.

4d-Flat Compactifications With Brane Vorticities

We present solutions in six-dimensional gravity coupled to a sigma model, in the presence of three-brane sources. The space transverse to the branes is a compact non-singular manifold. The example of O(3) sigma model in the presence of two three-branes is worked out in detail. We show that the four-dimensional flatness is obtained with a single condition involving the brane tensions, which are in general different and may be both positive, and another characteristic of the branes, vorticity. We speculate that the adjustment of the effective four-dimensional cosmological constant may occur through the exchange of vorticity between the branes. We then give exact instanton type solutions for sigma models targeted on a general Kähler manifold, and elaborate in this framework on multi-instantons of the O(3) sigma model. The latter have branes, possibly with vorticities, at the instanton positions, thus generalizing our two-brane solution.

Instanton contribution to scalar charmonium and glueball decays

We study instanton contributions to hadronic decays of the scalar glueball, the pseudoscalar charmonium state $\eta_c$, and the scalar charmonium state $\chi_c$. Hadronic decays of the $\eta_c$ are of particular interest. The three main decay channels are $K\bar{K}\pi$, $\eta\pi\pi$ and $\eta'\pi\pi$, each with an unusually large branching ratio $\sim 5%$. On the quark level, all three decays correspond to an instanton type vertex $(\bar{c}c)(\bar{s}s)(\bar{d}d)(\bar{u}u)$. We show that the total decay rate into three pseudoscalar mesons can be reproduced using an instanton size distribution consistent with phenomenology and lattice results. Instantons correctly reproduce the ratio $B(\pi\pi\eta)/B(\pi\pi\eta')$ but over-predict the ratio $B(K\bar{K}\pi)/B(\pi\pi\eta(\eta'))$. We consider the role of scalar resonances and suggest that the decay mechanism can be studied by measuring the angular distribution of decay products.

Pseudogaps in incommensurate charge density waves and one-dimensional semiconductors

We consider pseudogap effects for electrons interacting with gapless modes. We study generic 1D semiconductors with acoustic phonons and incommensurate charge density waves. We calculate the subgap absorption as it can be observed by means of photoelectron or tunneling spectroscopy. Within the formalism of functional integration and adiabatic approximation, the probabilities are described by nonlinear configurations of an instanton type. Particularities of both cases are determined by the topological nature of stationary excited states (acoustic polarons or amplitude solitons) and by the presence of gapless phonons that change the usual dynamics to the quantum dissipation regime. Below the free-particle edge, the pseudogap starts with an exponential (stretched exponential for gapful phonons) decrease of the transition rates. Deeply within the pseudogap, they are dominated by a power law, in contrast to a nearly exponential law for gapful modes.

Exotic Localized Coherent Structures of New (2+1)-Dimensional Soliton Equation**The project supported by National Natural Science Foundation of China

The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partial differential equation. Applying the Bäcklund transformation and introducing the arbitrary functions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types of solutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functions appropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the number of the peaks.

Theory of pseudogaps in charge density waves in application to photo electron spectroscopy

For a one-dimensional electron-phonon system we consider the photon absorption involving electronic excitations within the pseudogap energy range. Within the adiabatic approximation for the electron - phonon interactions these processes are described by ronlinear configurations of an instanton type. We calculate the subgap absorption as it can be observed by means of photo electron or tunneling spectroscopies. In details we consider systems with gapless modes: 1D semiconductors with acoustic phonons and incommensurate charge density waves. We found that below the free particle edge the pseudogap starts with the exponential decrease of transition rates changing to a power law deeply within the pseudogap, near the absolute edge.

Theory of subgap photoemission in one-dimensional electron-phonon systems: An instanton approach to pseudogaps

For a one-dimensional electron-phonon system we consider photon absorption involving electronic excitations within the pseudogap energy range. Within the adiabatic approximation for the electron-phonon interactions these processes are described by nonlinear configurations of an instanton type. The one-parameter ansatz for the extremal instanton trajectory allows one to span a wide spectral rang providing qualitatively correct limits. We calculate intensities of the photoemission spectroscopy (PES) including momentum-resolved or angle-resolved PES (ARPES), and supplement known results for the optical subgap absorption. We start with the generic case of a one-dimensional semiconductor with a pronounced polaronic effect. We consider in details the Peierls model for a half-filled band of electrons coupled to a lattice which describes the polyacethylene and some commensurate charge-density waves. Particular attention was required to study the momentum dependences for the ARPES, where we face an intriguing interference between the time evolution and the translational motion of the instantons.

Gravity waves from instantons

We perform a first principles computation of the spectrum of gravity waves produced in open inflationary universes. The background spacetime is taken to be the continuation of an instanton saddle point of the Euclidean no boundary path integral. The two-point tensor correlator is computed directly from the path integral and is shown to be unique and well behaved in the infrared. We discuss the tensor contribution to the cosmic microwave background anisotropy and show how it may provide an observational discriminant between different types of primordial instantons.

Symmetry analysis and exact solutions of the 2+1 dimensional sine-Gordon system

According to the space variable exchange symmetry, we change the 2+1 dimensional sine-Gordon system obtained by Konopelchenko and Rogers (KR) to a variant form. Some types of similarity reductions are obtained by using some Lie symmetry analysis. From these similarity reductions, we find that the soliton structure of the system possesses quite a rich structure. The line solitons parallel to the lines x+y=0 and x−y=0 may have an arbitrary shape. In addition to the well-known dromion solution, which is constructed by two line solitons, one may find many other kinds of soliton solutions localized in all directions. For instance, some kinds of ring type (basin-like, plateau-like and bowl-like) and instanton type soliton solutions, can be found directly by selecting the arbitrary functions included in the “single” soliton solution. The dromion solutions may also be constructed by straight line and curved line solitons.

Point-like instantons and the [formula omitted] heterotic string

We consider heterotic string theories compactified on a K3 surface which lead to an unbroken perturbative gauge group of Spin(32) Z 2 . All solutions obtained are combinations of two types of point-like instanton—one “simple type” as discovered by Witten and a new type associated to the “generalized second Stiefel-Whitney class” as introduced by Berkooz et al. The new type of instanton is associated to an enhancement of the gauge symmetry by Sp(4) and the addition of a massless tensor supermultiplet. It is shown that if four simple instantons coalesce at an orbifold point in the K3 surface then a massless tensor field appears which may be used to interpolate between the two types of instanton. By allowing various combinations of point-like instantons to coalesce, large gauge groups (e.g., rank 128) with many massless tensor supermultiplets result. The analysis is done in terms of F-theory.

Pair creation of black holes by domain walls.

In this paper we study the production of pairs of neutral and charged black holes by domain walls, finding classical solutions and calculating their classical actions. We find that neutral black holes whose creation is mediated by Euclidean instantons must be produced mutually at rest with respect to one another, but for charged black holes a new type of instanton is possible in which after formation the two black holes accelerate away from one another. These new types of instantons are not possible in Einstein-Maxwell theory with a cosmological constant. We also find that the creation of nonorientable black hole solutions can be mediated by Euclidean instantons and that in addition if one is prepared to consider entirely Lorentzian no-boundary-type contributions to the path integral then mutually accelerating pairs may be created even in the neutral case. Finally, we consider the production of Kaluza-Klein monopoles both by a standard cosmological term and in the presence of a domain wall. We find that compactification is accompanied by the production of pairs of Kaluza-Klein monopoles. \textcopyright{} 1996 The American Physical Society.

Quantum symmetries and stringy instantons

The quantum symmetry of many Landau-Ginzburg orbifolds appears to be broken by Yang-Mills instantons. However, isolated Yang-Mills instantons are not solutions of string theory: They must be accompanied by gauge anti-instantons, gravitational instantons, or topologically non-trivial configurations of the H field. We check that the configurations permitted in string theory do in fact preserve the quantum symmetry, as a result of non-trivial cancellations between symmetry breaking effects due to the various types of instantons. These cancellations indicate new constraints on Landau-Ginzburg orbifold spectra and require that the dilaton modulus mix with the twisted moduli in some Landau-Ginzburg compactifications. We point out that one can find similar constraints at all fixed points of the modular group of the moduli space of vacua.

Generalized spin systems and sigma models.

A generalization of the $SU(2)$--spin systems on a lattice and their continuum limit to an arbitrary compact group $G$ is discussed. The continuum limits are, in general, non--relativistic $\sigma$--model type field theories targeted on a homogeneous space $G/H$, where $H$ contains the maximal torus of $G$. In the ferromagnetic case the equations of motion derived from our continuum Lagrangian generalize the Landau--Lifshitz equations with quadratic dispersion relation for small wave vectors. In the antiferromagnetic case the dispersion law is always linear in the long wavelength limit. The models become relativistic only when $G/H$ is a symmetric space. Also discussed are a generalization of the Holstein--Primakoff representation of the $SU(N)$ algebra, the topological term and the existence of the instanton type solutions in the continuum limit of the antiferromagnetic systems.