Nyi Limit Research Articles

A new class of solutions of a generalized O(3)-sigma Chern-Simons model

In this work, we investigated the existence of compacton-like configuration in the O(3)-sigma model. We consider a minimally coupled O(3)-sigma model with a gauge field governed by a generalized Chern-Simons (CS) term. Contrary to that established in the literature, we impose a new set of boundary conditions and we find solutions to the variable fields and the respective energy density in the Bogomol'nyi limit. On the other hand, the introduction of a parameter ω in the Chern-Simons term can be adjusted to lead to finite-energy solutions of the model. Moreover, compact-like structures were studied with the evolution of this ω-generalized Chern-Simons term.

Solutions of coupled BPS equations for two-family Calogero and matrix models

We consider a large $N$, two-family Calogero and matrix model in the Hamiltonian, collective-field approach. The Bogomol'nyi limit appears and the solutions to the coupled Bogomol'nyi-Prasad-Sommerfeld equations are given by the static soliton configurations. We find all solutions close to constant and construct exact one-parameter solutions in the strong-weak dual case. Full classification of these solutions is presented.

Nonminimal Maxwell-Chern-Simons-O(3)−σvortices: Asymmetric potential case

In this work we study a nonlinear gauged $\mathrm{O}(3)\mathrm{\text{\ensuremath{-}}}\ensuremath{\sigma}$ model with both minimal and nonminimal coupling in the covariant derivative. Using an asymmetric scalar potential, the model is found to exhibit both topological and nontopological soliton solutions in the Bogomol'nyi limit.

Supermassive screwed cosmic string in dilaton gravity

The early universe might have undergone phase transitions at energy scales much higher than the one corresponding to the grand unified theories (GUT) scales. At these higher energy scales, the transition at which gravity separated from all other interactions, the so-called Planck era, more massive strings called supermassive cosmic strings could have been produced, with energy of about 1019 GeV. The dynamics of strings formed with this energy scale cannot be described by means of the weak-field approximation, as in the standard procedure for ordinary GUT cosmic strings. As suggested by string theories, at this extreme energy, gravity may be transmitted by some kind of scalar field (usually called the dilaton) in addition to the tensor field of Einstein's theory of gravity. It is then permissible to tackle the issue regarding the dynamics of supermassive cosmic strings within this framework. With this aim, we obtain the gravitational field of a supermassive screwed cosmic string in a scalar–tensor theory of gravity. We show that for the supermassive configuration, exact solutions of scalar–tensor screwed cosmic strings can be found in connection with the Bogomol'nyi limit. We show that the generalization of Bogomol'nyi arguments to the Brans–Dicke theory is possible when torsion is present and we obtain an exact solution in this supermassive regime, with the dilaton solution obtained by consistency with internal constraints.

2D Calogero model in the collective-field approach

We consider the large- N Calogero–Marchioro model in two dimensions in the Hamiltonian collective-field approach based on the 1 / N expansion. The Bogomol'nyi limit appears in the presence of the harmonic confinement. We investigate density fluctuations around the semiclassical uniform solution. The excitation spectrum splits into two branches depending on the value of the coupling constant. The ground state exhibits long-range order.

F-term strings in the Bogomolnyi limit are also BPS states

We derive the Bogomol'nyi equations for supersymmetric abelian F-term cosmic strings in four-dimensional flat space and show that, contrary to recent statements in the literature, they are BPS states in the Bogomol'nyi limit, but the partial breaking of supersymmetry is from N = 2. The second supersymmetry is not obvious in the N = 1 formalism, so we give it explicitly in components and in terms of a different set of N = 1 chiral superfields. We also discuss the appearance of a second supersymmetry in D-term models, and the relation to N = 2 F-term models. The analysis sheds light on an apparent paradox raised by the recent observation that D-term strings remain BPS when coupled to N = 1 supergravity, whereas F-term strings break the supersymmetry completely, even in the Bogomol'nyi limit. Finally, we comment on their semilocal extensions and their relevance to cosmology.

Nielsen-Olesen strings in Supersymmetric models

We investigate the behaviour of a model with two oppositely charged scalar fields. In the Bogomol'nyi limit this may be seen as the scalar sector of N=1 supersymmetric QED, and it has been shown that cosmic strings form. We examine numerically the model out of the Bogomol'nyi limit, and show that this remains the case. We then add supersymmetry-breaking mass terms to the supersymmetric model, and show that strings still survive. Finally we consider the extension to N=2 supersymmetry with supersymmetry-breaking mass terms, and show that this leads to the formation of stable cosmic strings, unlike in the unbroken case.

Systematics of flux tubes in the dual Ginzburg-Landau theory and Casimir scaling hypothesis: folklore and lattice facts

The ratios between string tensions $\sigma_D$ of color-electric flux tubes in higher and fundamental SU(3) representations, $d_{D} \equiv \sigma_{D}/\sigma_{\bf 3}$, are systematically studied in a Weyl symmetric formulation of the DGL theory. The ratio is found to depend on the Ginzburg-Landau (GL) parameter, $\kappa \equiv m_{\chi}/m_{B}$, the mass ratio between monopoles ($m_{\chi}$) and dual gauge bosons ($m_{B}$). While the ratios $d_{D}$ follow a simple flux counting rule in the Bogomol'nyi limit, $\kappa=1.0$, systematic deviations appear with increasing $\kappa$ due to interactions between fundamental flux inside a higher representation flux tube. We find that in a type-II dual superconducting vacuum near $\kappa = 3.0$ this leads to a consistent description of the ratios $d_{D}$ observed in lattice QCD simulations.

Generalized flux-tube solution in Abelian-projectedSU(N)gauge theory

The $[\mathrm{U}(1){]}^{N\ensuremath{-}1}$ dual Ginzburg-Landau (DGL) theory as a low-energy effective theory of Abelian-projected $\mathrm{SU}(N)$ gauge theory is formulated in a Weyl symmetric way. The string tensions of the flux-tube solutions of the DGL theory associated with color-electric charges in various representations of $\mathrm{SU}(N)$ are calculated analytically at the border between type I and type II of the dual superconducting vacuum (Bogomol'nyi limit). The resulting string tensions satisfy the flux counting rule, which reflects the non-Abelian nature of gauge theory.

Casimir scaling in a dual superconducting scenario of confinement

The string tensions of flux tubes associated with static charges in various SU(3) representations are studied within the dual Ginzburg-Landau (DGL) theory. The ratios of the string tensions between higher and fundamental representations, ${d}_{D}\ensuremath{\equiv}{\ensuremath{\sigma}}_{D}/{\ensuremath{\sigma}}_{F},$ are found to depend only on the Ginzburg-Landau (GL) parameter, $\ensuremath{\kappa}{=m}_{\ensuremath{\chi}}{/m}_{B},$ the mass ratio between monopoles ${m}_{\ensuremath{\chi}}$ and dual gauge bosons ${m}_{B}.$ In the case of the Bogomol'nyi limit $(\ensuremath{\kappa}=1),$ analytical values of ${d}_{D}$ are easily obtained by adopting the manifestly Weyl invariant formulation of the DGL theory, which are provided simply by the number of color-electric Dirac strings inside the flux tube. A numerical investigation of the ratio for various GL-parameter cases is also performed, which suggests that the Casimir scaling is obtained in the type-II parameter range within the interval $\ensuremath{\kappa}=5\ensuremath{\sim}9$ for various ratios ${d}_{D}.$

Simple models with Alice fluxes

We introduce two simple models which feature an Alice electrodynamics phase. In a well defined sense the Alice flux solutions we obtain in these models obey first order equations similar to those of the Nielsen–Olesen fluxtube [1] in the abelian Higgs model in the Bogomol'nyi limit. Some numerical solutions are presented as well.

Bogomol’nyi limit for magnetic vortices in a rotating superconductor

This work is the sequel of a previous investigation of stationary and cylindrically symmetric vortex configurations for simple models representing an incompressible non-relativistic superconductor in a rigidly rotating background. In the present paper, we carry out our analysis with a generalized Ginzburg-Landau description of the superconductor, which provides a prescription for the radial profile of the normal density within the vortex. Within this framework, it is shown that the Bogomol'nyi limit condition marking the boundary between type I and type II behavior is unaffected by the rotation of the background.

Weyl invariant formulation of the flux-tube solution in the dual Ginzburg-Landau theory

The flux-tube solution in the dual Ginzburg-Landau (DGL) theory in the Bogomol'nyi limit is studied by using the manifestly Weyl invariant form of the DGL Lagrangian. The dual gauge symmetry is extended to $[U(1)]_m^3$, and accordingly, there appear three different types of the flux-tube. The string tension for each flux-tube is calculated analytically and is found to be the same owing to the Weyl symmetry. It is suggested that the flux-tube can be treated in quite a similar way with the Abrikosov-Nielsen-Olesen vortex in the U(1) Abelian Higgs theory except for various types of flux-tube.

Hydrodynamics of Defects in the Abelian–Higgs Model: An Application to Nematic Liquid Crystals

The Abelian–Higgs model is the basis for a gauge covariant form of the distortion free energy for nematic liquid crystals. This is used to derive a new form of the Ericksen–Leslie equations incorporating the dynamics of disclinations in nematic films. The zero liquid flow case is treated in detail for simplicity. The equations are reduced to dynamic equations for disclination points in moduli space for a small deviation from the Bogomol'nyi limit. We are able to derive analytically the dynamics of disclinations with winding numbers of the same sign. A set of such disclinations close to one another, i.e., with overlapping cores, can result from the disintegration of a larger disclination, and they repel one another. For a pair of such dis- clinations far apart from one another we find that they move on a straight line where their separation increases logarithmically over time.

Conservation laws in a first-order dynamical system of vortices

The conservation laws for linear and angular momenta in a Schrödinger-Chern-Simons field theory modelling vortex dynamics in planar superconductors are studied. In analogy with fluid vortices it is possible to express the linear and angular momenta as low moments of vorticity. The conservation laws are shown to be consistent with those obtained in the moduli space approximation for vortex dynamics, valid close to the Bogomol'nyi limit. For Bogomol'nyi vortices, the relevant moments of vorticity can be evaluated fairly explicitly, as can the integral of log||2, where is the scalar field. Conservation of angular momentum prevents a single vortex from escaping to infinity.

Z3strings and their interactions

We construct ${Z}_{3}$ vortex solutions in a model in which $\mathrm{SU}(3)$ is spontaneously broken to ${Z}_{3}.$ The model is truncated to one in which there are only two dimensionless free parameters and the interaction of vortices within this restricted set of models is studied numerically. We find that there is a curve in the two dimensional space of parameters for which the energy of two asymptotically separated vortices equals the energy of the vortices at vanishing separation. This suggests that the inter-vortex potential for ${Z}_{3}$ strings might be flat for these couplings, much like the case of $U(1)$ strings in the Bogomol'nyi limit. However, we argue that the intervortex potential is attractive at short distances and repulsive at large separations leading to the possibility of unstable bound states of ${Z}_{3}$ vortices.

Multi-vortex solution in the Sutherland model

We consider the large-$N$ Sutherland model in the Hamiltonian collective-field approach based on the $1/N$ expansion. The Bogomol'nyi limit appears and the corresponding solutions are given by static-soliton configurations. They exist only for $l<1$, i.e. for the negative coupling constant of the Sutherland interaction. We determine their creation energies and show that they are unaffected by higher-order corrections. For $l=1$, the Sutherland model reduces to the free one-plaquette Kogut-Susskind model.

Chaos and stability of Nielsen-Olesen vortex solution with cylindrical symmetry at critical coupling

The chaotic properties of the Nielsen-Olesen vortex solution with cylindrical symmetry in the Abelian-Higgs theories are numerically studied at a critical coupling constant at which the type of the interaction between vortices changes. From the step-wise behaviour of maximal Lyapunov exponents of fields it is shown that the solution exhibits chaos in the case of large perturbation, whose gross structure is similar to the order-to-chaos transition observed in several topological solutions of the SU(2) Yang-Mills-Higgs theories. It is suggested that the time evolution of the system might cause some change in the interaction between the vortices with winding number bigger than one at Bogomol'nyi limit.

Solitons in the Calogero-Sutherland collective-field model

In the Bogomol'nyi limit of the Calogero-Sutherland collective-field model we find static-soliton solutions. The solutions of the equations of motion are moving solitons, having no static limit for λ > 1. They behave like holes and lumps, depending on the value of the statistical parameter λ. We interpret these soliton solutions as effectively made of one quasi-particle and one quasi-hole excitation.

Remarks on gauge vortex scattering

In the abelian Higgs model, among other situations, it has recently been realized that the head-on scattering of n solitons distributed symmetrically around the point of scattering is by an angle π n , independent of various details of the scattering. In this note, it is first observed that this result is in fact not entirely surprising: the above is one of only two possible outcomes. Then, a generalization of an argument given by Ruback for the case of two gauge theory vortices in the Bogomol'nyi limit is used to show that in the geodesic approximation the above result follows from purely geometric considerations.