Topological energy bounds in generalized Skyrme models

Adam, C.; Wereszczyński, A.

doi:10.1103/physrevd.89.065010

Cited by 36 publications

(29 citation statements)

References 71 publications

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“…In particular, in the limit of large n and fixed L, the energy of the multi-Skyrmions grows as n 2 , as shown in Fig. 3 (A similar behavior has been found in a modified version of the Skyrme model [25]). These multi-Skyrmion form regular patterns along x, as in Fig.…”

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confidence: 51%

Exact multisoliton solutions in the four-dimensional Skyrme model

2014

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In spite of all this, until very recently no exact analytic solutions of the Skyrme model with non-trivial topological charges were known. One of the reasons is that the Skyrme-BPS bound on the energy cannot be saturated for non-trivial spherically symmetric configurations [14]. Nevertheless, many rigorous results about Skyrmions dynamics have been derived, see for instance [15][16][17].The action of the SU (2) Skyrme system in four dimensional spacetime iswhereHere t i are the SU (2) generators and we set the units = c = 1. The coupling constants K > 0 and λ > 0 are fixed by comparison with experimental data [6]. The presence of the first term of the Skyrme action (1), is mandatory to describe pions while the second is the only covariant term leading to second order field equations in time which supports the existence of Skyrmions in four dimensions.In the present paper, exact spherically symmetric solutions of the Skyrme model with both a non-trivial winding number and a finite soliton mass (topological charge) are presented. Using the formalism introduced in [18][19][20], it is shown that although the BPS bound in terms of the winding cannot be saturated, a new topological charge exists that can be saturated corresponding to a different BPS bound. The baryon number is the homotopy of the space into the group. The simplest choice would be to consider the curved background S 3 as physical space, as already considered in the pioneering papers [21,22]. The second natural choice of special sections with integer homotopy into SU (2) is S 1 × S 2 (or R × S 2 ). This can be represented by a metric of the formIn simple words, this geometry describes tridimensional cylinders whose sections are S 2 spheres of area 4πR 2 0 . The physical meaning of R 0 is that it takes into account finite volume effects. One could put the Skyrme action into, say, a cube. However, this way of proceeding often breaks symmetries. On the other hand, a spherical box of finite radius would lead to difficulties in requiring the Skyrmions approach the identity at the boundary. Therefore, it is much more convenient to choose a metric which at the same time takes into account finite volume effects and keeps the spherical symmetry. We are able construct exact Skyrmions in a finite volume but, instead of putting by hand a cut-off on the coordinates, we leave this task to the geometry. Besides, this geometry is such that the group of the isometries of (2) contains SO(3) as a subgroup and so it includes the spherical symmetry of the Skyrmion in flat space. This fact allows examining how far is the BPS bound from being saturated and to construct an energy bound which can in fact be saturated. This could be of interest both in high energy and solid state physics whose features, after the papers [21,22], have not been thoroughly investigated from the analytical viewpoint.In order to construct the exact solution of the Skyrme model, the following standard parametrization of the

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confidence: 51%

Exact multisoliton solutions in the four-dimensional Skyrme model

2014

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“…6. Indeed, it was shown by Adam and Wereszczynski [23] that for the L 26 submodel the new energy bound is…”

Section: Modelmentioning

confidence: 97%

Crystal structures in generalized Skyrme model

Perapechka

Shnir

2017

Phys. Rev. D

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We investigate the properties of triply-periodic Skyrme crystals in the generalized Skyrme model $\mathcal{L}_6 + \mathcal{L}_4 + \mathcal{L}_2+ \mathcal{L}_0$ with higher-derivative terms up to sixth order. Three different symmetry breaking potential terms $\mathcal{L}_0$ are considered, the generalized pion mass term, double vacuum potential and mixed potential. Various scenario of phase transitions from the low density phase to the high density phase are examined for different choices of the parameters of the model. In particular, we investigated limiting behavior of the Skyrme crystals in the truncated submodel without the Skyrme term $\mathcal{L}_4$ and/or without the $\mathcal{L}_2$ term. We show that the Skyrme crystal may exist in the pure $\mathcal{L}_4$ and $\mathcal{L}_6$ models and investigated the phase structure of these solutions. Considering the near-BPS submodel, we found that there are indications of the phase transition from a low density quasi-liquid phase to the high density symmetric phase of the Skyrmionic matter.Comment: 18 pages, 9 figure

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“…The lightly bound Skyrme model is based on an energy bound [17,23] for the Skyrme term and a potential to the fourth power. Although this model has a saturable solution in the 1-Skyrmion sector, no solutions saturate the bound for higher topological degrees.…”

Section: Introductionmentioning

confidence: 99%

Exploring the generalized loosely bound Skyrme model

Gudnason¹

2018

Phys. Rev. D

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The Skyrme model is extended with a sextic derivative term -called the BPS-Skyrme term -and a repulsive potential term -called the loosely bound potential. A large part of the model's parameter space is studied for the 4-Skyrmion which corresponds to the Helium-4 nucleus and emphasis is put on preserving as much of the platonic symmetries as possible whilst reducing the binding energies. We reach classical binding energies for Helium-4 as low as 0.2%, while retaining the cubic symmetry of the 4-Skyrmion, and after taking into account the quantum mass correction to the nucleon due to spin/isospin quantization, we get total binding energies as low as 3.6% -still with the cubic symmetry intact.

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Topological energy bounds in generalized Skyrme models

Cited by 36 publications

References 71 publications

Exact multisoliton solutions in the four-dimensional Skyrme model

Exact multisoliton solutions in the four-dimensional Skyrme model

Crystal structures in generalized Skyrme model

Exploring the generalized loosely bound Skyrme model

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