B=3 Tetrahedrally Symmetric Solitons in the Chiral Quark Soliton Model

In this paper, B=3 soliton solutions with tetrahedral symmetry are obtained numerically in the chiral quark soliton model using the rational map ansatz. The solution exhibits a triply degenerate bound spectrum of the quark orbits in the background of tetrahedrally symmetric pion field configuration. The corresponding baryon density is tetrahedral in shape. Our numerical technique is independent on the baryon number and its application to $B \geq 4$ is straightforward.Comment: 4 pages, 3 figure

Hopf Soliton Solutions from Low Energy Effective Action of SU(2) Yang-Mills Theory

The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) $\sigma$ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains another fourth-order term which destabilizes the soliton solution. In this paper we derive an extended action including second derivative terms and obtain soliton solutions numerically. A new topological lower bound formula is infered for the extended action.Comment: 18 pages, 7 figure

Collective quantization of axially symmetric gravitating B=2 skyrmion

In this paper we perform collective quantization of an axially symmetric skyrmion with baryon number two.The rotational and isorotational modes are quantized to obtain the static properties of a deuteron and other dibaryonic objects such as masses, charge densities, magnetic moments. We discuss how the gravity affects to those observables.Comment: 13 pages, 13 figures, 1 table, accepted to Physical Review

Quantized Solitons in the Extended Skyrme-Faddeev Model

The construction of axially symmetric soliton solutions with non-zero Hopf topological charges according to a theory known as the extended Skyrme-Faddeev model, was performed in [1]. In this paper we show how masses of glueballs are predicted within this model

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.Comment: 16 pages, 17 figures. One figure added, some points clarified, references improved. Version accepted for publicatio

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.Comment: 22 pages, 42 figures, minor correction

Regular and Black Hole Solutions in the Einstein-Skyrme Theory with Negative Cosmological Constant

We study spherically symmetric regular and black hole solutions in the Einstein-Skyrme theory with a negative cosmological constant. The Skyrme field configuration depends on the value of the cosmological constant in a similar manner to effectively varying the gravitational constant. We find the maximum value of the cosmological constant above which there exists no solution. The properties of the solutions are discussed in comparison with the asymptotically flat solutions. The stability is investigated in detail by solving the linearly perturbed equation numerically. We show that there exists a critical value of the cosmological constant above which the solution in the branch representing unstable configuration in the asymptotically flat spacetime turns to be linearly stable.Comment: 10 pages, 9 figures, comments and one reference added, to appear in Class.Quant.Gra

Glueball mass from quantized knot solitons and gauge-invariant gluon mass

We propose an approach which enables one to obtain simultaneously the glueball mass and the gluon mass in the gauge-invariant way to shed new light on the mass gap problem in Yang-Mills theory. First, we point out that the Faddeev (Skyrme--Faddeev-Niemi) model can be induced through the gauge-invariant vacuum condensate of mass dimension two from SU(2) Yang-Mills theory. Second, we obtain the glueball mass spectrum by performing the collective coordinate quantization of the topological knot soliton in the Faddeev model. Third, we demonstrate that a relationship between the glueball mass and the gluon mass is obtained, since the gauge-invariant gluon mass is also induced from the relevant vacuum condensate. Finally, we determine physical values of two parameters in the Faddeev model and give an estimate of the relevant vacuum condensation in Yang-Mills theory. Our results indicate that the Faddeev model can play the role of a low-energy effective theory of the quantum SU(2) Yang-Mills theory.Comment: 17 pages, 2 figures, 3 tables; a version accepted for publication in J. Phys. A: Math. Gen.; Sect. 2 and sect. 5 (old sect. 4) are modified. Sect. 4, Tables 1 and Table 3 are adde

Dual Spaces of Resonance In Thick p−p-Branes

In this work we consider $q-$form fields in a $p-$brane embedded in a $D=(p+2)$ space-time. The membrane is generated by a domain wall in a Randall-Sundrum-like scenario. We study conditions for localization of zero modes of these fields. The expression agrees and generalizes the one found for the zero, one, two and three-forms in a $3-$brane. By a generalization we mean that our expression is valid for any form in an arbitrary dimension with codimension one. We also point out that, even without the dilaton coupling, some form fields are localized in the membrane. The massive modes are considered and the resonances are calculated using a numerical method. We find that different spaces have identical resonance structures, which we call dual spaces of resonances(DSR).Comment: 15 page