arXiv subjects

Nobuyuki Sawado

Publications and source records attributed to Nobuyuki Sawado.

At least 37 records · Page 2Linked to original sources

arXiv2018

Soliton solutions of the fermion-Skyrmion system in (2+1) dimensions

We study effects of backreaction of the fermionic modes localized by the baby Skyrmion in the (2+1)-dimensional Skyrme model. It is shown that there is a tower of fermionic modes of two different types, localized by the soliton, however there is only one fermionic level, which flows from positive to negative value as coupling increases. Considering the strong coupling regime we observe that the coupling of the bosonic field to the fermions may strongly deform the Skyrmion, in particular the regions of negative topological charge density appear.

hep-th↗

arXiv2018

BPS Sphalerons in the $F_2$ Non-Linear Sigma Model

We construct static and also time-dependent solutions in a non-linear sigma model with target space being the flag manifold $F_2=SU(3)/U(1)^2$ on the four dimensional Minkowski space-time by analytically solving the second order Euler-Lagrange equation. We show the static solutions saturate an energy lower bound and can be derived from coupled first order equations though they are saddle point solutions. We also discuss basic properties of the time-dependent solutions.

hep-th↗

arXiv2016

Black hole Skyrmion in a generalized Skyrme model

We study a Skyrme-like model with the Skyrme term and a sixth-order derivative term as higher-order terms, coupled to gravity and we construct Schwarzschild black hole Skyrme hair. We find, surprisingly, that the sixth-order derivative term alone cannot stabilize the black hole hair solutions; the Skyrme term with a large enough coefficient is a necessity.

hep-th↗

arXiv2016

Collective coordinate quantization and spin statistics of the solitons in the $\mathbb{C}P^N$ Skyrme-Faddeev model

The $\mathbb{C}P^N$ extended Skyrme-Faddeev model possesses planar soliton solutions. We consider quantum aspects of the solutions applying collective coordinate quantization in regime of rigid body approximation. In order to discuss statistical properties of the solutions we include an Abelian Chern-Simons term (the Hopf term) in the Lagrangian. Since $Π_3(\mathbb{C}P^1)=\mathbb{Z}$ then for $N=1$ the term becomes an integer. On the other hand for $N>1$ it became perturbative because $Π_3(\mathbb{C}P^N)$ is trivial. The prefactor of the Hopf term (anyon angle) $Θ$ is not quantized and its value depends on the physical system. The corresponding fermionic models can fix value of the angle $Θ$ for all $N$ in a way that the soliton with $N=1$ is not an anyon type whereas for $N>1$ it is always an anyon even for $Θ=nπ, n\in \mathbb{Z}$. We quantize the solutions and calculate several mass spectra for $N=2$. Finally we discuss generalization for $N\geqq 3$.

hep-th↗

arXiv2015

Gravitating BPS Skyrmions

The BPS Skyrme model has many exact analytic solutions in flat space. We generalize the model to a curved space or spacetime and find that the solutions can only be BPS for a constant time-time component of the metric tensor. We find exact solutions on the curved spaces: a 3-sphere and a 3-hyperboloid; and we further find an analytic gravitating Skyrmion on the 3-sphere. For the case of a nontrivial time-time component of the metric, we suggest a potential for which we find analytic solutions on anti-de Sitter and de Sitter spacetimes in the limit of no gravitational backreaction. We take the gravitational coupling into account in numerical solutions and show that they are well approximated by the analytic solutions for weak gravitational coupling.

hep-th↗

arXiv2015

Potentials and the vortex solutions in the $CP^N$ Skyrme-Faddeev model

The extended Skyrme-Faddeev model possesses vortex solutions in a (3+1) dimensional Minkowski space-time with target space $CP^N$. They have finite energy per unit of length and contain waves propagating along vortices with the speed of light. We introduce various types of the potentials which correspond with holomorphic solutions of the integrable sector and also with several numerical solutions outside of this sector. The presented solutions constitute a strong indication that the current model contains large class of solutions with much wider range of coupling constants than the previously known exact solution.

hep-th↗

arXiv2014

Exact, molecular-shaped vortices with fractional and integer charges in the extended Skyrme-Faddeev model

We analytically construct vortex solutions in the integrable sector of the extended Skyrme-Faddeev model. The solutions are holomorphic type which satisfy the zero curvature condition. For the model parameter $βe^2=1$ there is a lump solution, and for $βe^2 \neq 1$ new potentials are introduced for the several molecular-shaped solutions with half-integer or integer charges. They necessarily have infinite number of conserved currents and some of the examples are shown. By performing an annealing simulation with our potentials, we verify the existence of the solutions of the integrable sector.

hep-th↗

arXiv2014

Aspects of $C_3$-symmetric calorons from numerical Nahm transform

Calorons are finite action solutions to the anti-selfdual Yang-Mills equations on $\mathbb{R}^3\times S^1$. They are generally constructed by the so called Nahm construction. We perform the numerical Nahm transform for the Nahm data of 3-calorons with $C_3$-symmetry, which do not have the monopole limits. Dissimilar to the cases of having monopole limits, we can trace the zero-circumference limit of $S^1$.It is found that the action density of the calorons tends to fade away as $S^1$ shrinks.

hep-th↗

arXiv2012

Vortices in the extended Skyrme-Faddeev model

We construct analytical and numerical vortex solutions for an extended Skyrme-Faddeev model in a $(3+1)$ dimensional Minkowski space-time. The extension is obtained by adding to the Lagrangian a quartic term, which is the square of the kinetic term, and a potential which breaks the SO(3) symmetry down to SO(2). The construction makes use of an ansatz, invariant under the joint action of the internal SO(2) and three commuting U(1) subgroups of the Poincaré group, and which reduces the equations of motion to an ODE for a profile function depending on the distance to the $x^3$-axis. The vortices have finite energy per unit length, and have waves propagating along them with the speed of light. The analytical vortices are obtained for special choice of potentials, and the numerical ones are constructed using the Successive Over Relaxation method for more general potentials. The spectrum of solutions is analyzed in detail, specially its dependence upon special combinations of coupling constants.

hep-th↗

arXiv2012

Cyclic Calorons

The Nahm data of periodic instantons, often called calorons, with spatial $C_N$-symmetries are considered, by applying Sutcliffe's ansatz for the monopoles with $C_N$-symmetries. The bulk data of calorons are shown to enjoy the periodic Toda lattice, and the solutions are given in terms of elliptic theta functions. The case of N=3 calorons are investigated in detail. It is found that the "scale parameters" of these calorons have upper bounds in their values, so that they do not have the large scale, or monopole, limits. The instanton limit of the $C_3$-symmetric caloron is obtained.

hep-th↗

arXiv2012

Non-axisymmetric baby-skyrmion branes

We investigate the existence of non axisymmetric solutions in the 6-dimensional baby-Skyrme brane model. The brane is described by a localized solution to the baby-Skyrme model extending in the extra dimensions. Such non symmetric branes have already been constructed in the original 2+1-dimensional baby-Skyrme model in flat space. We generalize this result to the case of gravitating baby-Skyrme and in the context of extradimensions. These non-trivial deformation from the axisymmetric shape appear for higher values of the topological charge, so we consider the cases of $B=3,4$, where $B$ is the topological charge. We solve the coupled system of the Einstein and baby-Skyrme equations by successive over relaxation method. We argue that the result may be a possible resolution for the fermion mass hierarchy puzzle.

hep-th↗

arXiv2012

Localizing modes of massive fermions and a U(1) gauge field in the inflating baby-skyrmion branes

We consider the six dimensional brane world model, where the brane is described by a localized solution to the baby-Skyrme model extending in the extradimensions. The branes have a cosmological constant modeled by inflating four dimensional slices and we further consider a bulk cosmological constant. We focus on the topological number three solutions and discuss the localization mechanism of the fermions on the above 3-branes. We discuss interpretation of the model in term of quark third generation mass and in terms of the inflation history. We argue that it is possible to track the phases of inflation in our model by suitably choosing the parameters. We further discuss the localization properties of gauge fields on the brane and argue that this is achieved only for specific values of the electromagnetic coupling, providing a quantization to the electric charge.

gr-qc↗

arXiv2011

Numerical Nahm transform for 2-caloron solutions

A new numerical method for performing the Nahm transform for charge $k=2$ caloron is presented. The Weyl equations with boundary impurities are solved directly and the determination of the appropriate basis to the linear system is established. The action densities of the 2-calorons with 10 moduli parameters are shown.

hep-th↗

arXiv2010

Inflating baby-Skyrme branes in six dimensions

We consider a six dimensional brane world model, where the brane is described by a localized solution to the baby-Skyrme model extending in the extradimensions. The branes have a cosmological constant modeled by inflating four dimensional slices and we further consider a bulk cosmological constant. We construct solutions numerically and present evidences that the solutions cease to exist for large values of the brane cosmological constant in some particular case. Then we study the stability of the model by considering perturbation of the gravitational part (resp. baby skyrmion) with fixed matter fields (resp. gravitational background). Our results indicate that the perturbation equations do not admit localized solutions for certain type of perturbation. The stability analysis can be alternatively seen as leading to a particle spectrum; we give mass estimations for the baby-Skyrme perturbation and for the graviton.

hep-th↗

arXiv2009

Static Hopfions in the extended Skyrme-Faddeev model

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is an extension of the Skyrme-Faddeev model by the addition of a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled non-linear partial differential equations in two variables by a successive over-relaxation (SOR) method. We construct numerical solutions with Hopf charge up to four, and calculate their analytical behavior in some limiting cases. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms. Their energies and sizes tend to zero as that combination approaches a particular special value. We calculate the equivalent of the Vakulenko and Kapitanskii energy bound for the theory and find that it vanishes at that same special value of the coupling constants. In addition, the model presents an integrable sector with an infinite number of local conserved currents which apparently are not related to symmetries of the action. In the intersection of those two special sectors the theory possesses exact vortex solutions (static and time dependent) which were constructed in a previous paper by one of the authors. It is believed that such model describes some aspects of the low energy limit of the pure SU(2) Yang-Mills theory, and our results may be important in identifying important structures in that strong coupling regime.

hep-th↗

arXiv2009

Localization of massive fermions on the baby-skyrmion branes in 6 dimensions

We construct brane solutions in 6 dimensional Einstein-Skyrme systems. A class of baby skyrmion solutions realizes warped compactification of the extra dimensions and gravity localization on the brane for negative bulk cosmological constant. Coupling of the fermions with the brane skyrmions lead to the brane localized fermions. In terms of the level crossing picture, emergence of the massive localized modes as well as the zero mode are observed. Nonlinear nature of the skyrmions brings richer information for the fermions level structure. The level comprises doubly degenerate lowest plus single excited modes. The three generation of the fundamental fermions is based on this structure. The quark/lepton mass hierarchy is successfully obtained in terms of a slightly deformed baby-skyrmions with topological charge three.

hep-th↗

arXiv2008

Fermions in gravity and the skyrmion backgrounds in six dimensional brane-worlds

We construct brane solutions in six dimensional Einstein-Skyrme systems. A class of baby skyrmion solutions realize warped compactification of the extra dimensions and gravity localization on the brane for negative bulk cosmological constant. Coupling of the fermions with the brane skyrmions successfully lead to the brane localized fermions. The standard representation of the gamma matrices is used to obtain massive localized modes as well as the massless one. Nonlinear nature of the skyrmions brings richer information for the fermions level structure. In terms of the level crossing picture, emergence of the massive localized modes as well as the zero mode are observed.

hep-th↗

arXiv2008

Localizing gravity on Maxwell gauged CP1 model in six dimensions

We shall consider about a 3-brane embedded in six-dimensional space-time with a negative bulk cosmological constant. The 3-brane is constructed by a topological soliton solution living in two-dimensional axially symmetric transverse subspace. Similar to most previous works of six-dimensional soliton models, our Maxwell gauged CP1 brane model can also achieve to localize gravity around the 3-brane. The CP1 field is described by a scalar doublet and derived from O(3) sigma model by projecting it onto two-dimensional complex space. In that sense, our framework is more effective than other solitonic brane models concerning with gauge theory. We shall also discuss about linear stability analysis for our new model by fluctuating all fields.

hep-th↗