Skyrmions in the presence of isospin chemical potential

Ponciano, Juan A.; Scoccola, N. N.

doi:10.1016/j.physletb.2007.11.047

Cited by 15 publications

(17 citation statements)

References 22 publications

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“…As it is well known, the presence of the isospin chemical potential is encoded in the following covariant derivative (see [28] [29] [30] [31])…”

Section: Iii12 Inclusion Of Chemical Potential and Infinite Volumementioning

confidence: 99%

“…In particular, the lack of explicit solutions with topological charge on flat space-times made very difficult the analysis of the corresponding phase diagram. Early important results (based on the original spherical Skyrmion 1 ) analyzing finite density effects as well as the role of the Isospin chemical potential can be found in [27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

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Analytic topologically nontrivial solutions of the ( 3+1 )-dimensional U(1) gauged Skyrme model and extended duality

et al. 2017

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We construct the first analytic examples of topologically non-trivial solutions of the (3+1)dimensional U (1) gauged Skyrme model within a finite box in (3+1)-dimensional flat space-time. There are two types of gauged solitons. The first type corresponds to gauged Skyrmions living within a finite volume. The second corresponds to gauged time-crystals (smooth solutions of the U (1) gauged Skyrme model whose periodic time-dependence is protected by a winding number). The notion of electromagnetic duality can be extended for these two types of configurations in the sense that the electric and one of the magnetic components can be interchanged. These analytic solutions show very explicitly the Callan-Witten mechanism (according to which magnetic monopoles may "swallow" part of the topological charge of the Skyrmion) since the electromagnetic field contribute directly to the conserved topological charge of the gauged Skyrmions. As it happens in superconductors, the magnetic field is suppressed in the core of the gauged Skyrmions. On the other hand, the electric field is strongly suppresed in the core of gauged time crystals.

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“…As it is well known, the presence of the isospin chemical potential is encoded in the following covariant derivative (see [28] [29] [30] [31])…”

Section: Iii12 Inclusion Of Chemical Potential and Infinite Volumementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytic topologically nontrivial solutions of the ( 3+1 )-dimensional U(1) gauged Skyrme model and extended duality

et al. 2017

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“…The Baryon number corresponding to the Skyrme ansatz in Eqs. (15) and (16) and to the gauge potential in Eq. (17) is…”

Section: Gauged Skyrmionsmentioning

confidence: 99%

“…One of the problematic consequences of this fact is that the analysis of the phase diagram is quite difficult. In particular, analytic results on finite density effects and on the role of the Isospin chemical potential were unavailable despite the huge efforts in the pioneering references [11], [12], [13], [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Analytic ( 3+1 )-dimensional gauged Skyrmions, Heun, and Whittaker-Hill equations and resurgence

Canfora

Lagos

et al. 2018

Phys. Rev. D

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We show that one can reduce the coupled system of seven field equations of the (3+1)-dimensional gauged Skyrme model to the Heun equation (which, for suitable choices of the parameters, can be further reduced to the Whittaker-Hill equation) in two non-trivial topological sectors. Hence, one can get a complete analytic description of gauged solitons in (3+1) dimensions living within a finite volume in terms of classic results in the theory of differential equations and Kummer's confluent functions. We consider here two types of gauged solitons: gauged Skyrmions and gauged timecrystals (namely, gauged solitons periodic in time, whose time-period is protected by a winding number). The dependence of the energy of the gauged Skyrmions on the Baryon charge can be determined explicitly. The theory of Kummer's confluent functions leads to a quantization condition for the period of the time-crystals. Likewise, the theory of Sturm-Liouville operators gives rise to a quantization condition for the volume occupied by the gauged Skyrmions. The present analysis also discloses that resurgent techniques are very well suited to deal with the gauged Skyrme model as well. In particular, we discuss a very nice relation between the electromagnetic perturbations of the gauged Skyrmions and the Mathieu equation which allows to use many of the modern resurgence techniques to determine the behavior of the spectrum of these perturbations.

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“…Some numerical results with the use of the spherical Skyrme ansatz are presented in [24,25,26,27,28] and references therein. Due to the fact that both finite volume effects and isospin chemical potential break spherical symmetry it is extremely difficult to improve the pioneering results in [24,25,26,27,28] without changing the original Skyrme ansatz. The main problem in this group is certainly the compression modulus [33,34,35] (to be defined precisely in the next section) which, roughly speaking, has to do with the derivative of the total energy of the Skyrmions with respect to the volume.…”

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confidence: 99%

Analytic studies of static and transport properties of (gauged) Skyrmions

2019

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We study static and transport properties of Skyrmions living within a finite spatial volume in a flat (3+1)-dimensional spacetime. In particular, we derive an explicit analytic expression for the compression modulus corresponding to these Skyrmions living within a finite box and we show that such expression can produce a reasonable value. The gauged version of these solitons can be also considered. It is possible to analyze the order of magnitude of the contributions to the electrons conductivity associated to the interactions with this Baryonic environment. The typical order of magnitude for these contributions to conductivity can be compared with the experimental values of the conductivity of layers of Baryons.analytic solution was available. Nevertheless, many numerical studies have shown that the Skyrme model provides results in good agreement with experiments.Despite the success of the model and the existence of several solutions among different contexts, the analysis of their phenomenological aspects seldom can be carried out in an analytic manner. For an analytic solution and a relevant study in compact manifolds see [16]. The gauged Skyrme model (which describes the coupling of a U (1) gauge field with the Skyrme theory) has also very important applications in the analysis of electromagnetic properties of Baryons, in the decay of nuclei in presence of defects (see [8,17,18,19,20,21] and references therein). Obviously, from the point of view of constructing analytic solutions, the U (1) gauged Skyrme model is even worse than the original Skyrme theory. Until very recently, no explicit topologically non-trivial solution was available. Thus, topological configurations of this theory have been deeply analyzed numerically (see [22,23] and references therein).Here we list three relevant problems in the applications of (gauged) Skyrme theory to high energy phenomenology which will be the focus of the present paper.1) Finite density effects and the compression modulus: Finite density effects (and, in general, the phase diagrams) in the Skyrme model have been historically a very difficult topic to analyze with analytic methods. The lack of explicit solutions with topological charge living within a finite flat box with the spherical Skyrme ansatz is the origin of the problem. Some numerical results with the use of the spherical Skyrme ansatz are presented in [24,25,26,27,28] and references therein. Due to the fact that both finite volume effects and isospin chemical potential break spherical symmetry it is extremely difficult to improve the pioneering results in [24,25,26,27,28] without changing the original Skyrme ansatz. The main problem in this group is certainly the compression modulus [33,34,35] (to be defined precisely in the next section) which, roughly speaking, has to do with the derivative of the total energy of the Skyrmions with respect to the volume. The experimental value is different from the value derived using the original spherical hedgehog ansatz. The usual way to compute the compression modulus ...

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Skyrmions in the presence of isospin chemical potential

Cited by 15 publications

References 22 publications

Analytic topologically nontrivial solutions of the ( 3+1 )-dimensional U(1) gauged Skyrme model and extended duality

Analytic topologically nontrivial solutions of the ( 3+1 )-dimensional U(1) gauged Skyrme model and extended duality

Analytic ( 3+1 )-dimensional gauged Skyrmions, Heun, and Whittaker-Hill equations and resurgence

Analytic studies of static and transport properties of (gauged) Skyrmions

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