BPS submodels of the generalized Skyrme model and how to find them

Atmaja, Ardian Nata; Gunara, Bobby Eka; Prasetyo, Ilham

doi:10.1016/j.nuclphysb.2020.115062

Cited by 8 publications

(10 citation statements)

References 34 publications

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“…It has also been used to find the BPS monopoles and dyons in various SU(2) Yang-Mills-Higgs models in the four-dimensional spacetime [25,26]. The reason for using this method is that it has been successfully used to find the BPS skyrmions in some (genuine and nongenuine) submodels of the generalized Skyrme model in the four-dimensional spacetime [27]. 1 Two main cases considered here are the spherically symmetric and non-spherically symmetric cases, which are defined to be the symmetry of the static energy density in a particular ansatz.…”

Section: Jhep07(2021)090mentioning

confidence: 99%

“…Because the derivative terms in the effective Lagrangian density (3.4) contain only the first derivative of ξ, or ξ , the BPS-Lagrangian method in [27] suggests that the corresponding L BPS should take the following form…”

Section: Jhep07(2021)090 3 Bps Skyrme Submodels In the Spherically Symmetric Lagrangian Densitymentioning

confidence: 99%

“…In this section, we consider the ansatz (2.14) without fixing all the effective fields. It is easy to see that the effective Lagrangian (2.15) also depends explicitly on the polar coordinate θ besides the radial coordinate r. In this case, we use the prescription in [27] as such the general BPS Lagrangian density has the form…”

Section: Bps Skyrme Submodel In the Non-spherically Symmetric Lagrangian Densitymentioning

confidence: 99%

“…This solution has total static energy given by (4.28). According to the prescription in [27], there could be other possible (genuine) BPS submodels of the effective Lagrangian density (2.15), which consist of four derivative terms. However, we found that those submodels do not have Bogomolny's equations as shown in the appendix.…”

Section: Jhep07(2021)090mentioning

confidence: 99%

“…The two main cases that have been considered, based on the effective Lagrangian density of the BPS submodels, are the spherically symmetric and the non-spherically symmetric cases. Employing the BPS Lagrangian method, we followed the prescription in [27] for the BPS Lagrangian density. In the spherically symmetric case, where only the effective field ξ in the ansatz (2.14) is undetermined, we found there are only two possible BPS submodels which are the submodel with λ 0 = λ 1 = λ 3 = λ 4 = 0, or namely the Skyrme term, and the submodel with λ 1 = λ 2 = λ 3 = 0, the potential term and a term that is proportional to the square of the topological current.…”

Section: Jhep07(2021)090 5 Conclusionmentioning

confidence: 99%

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BPS Skyrme submodels of the five-dimensional Skyrme model

Fadhilla

Gunara

Atmaja

2021

J. High Energ. Phys.

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In this paper, we search for the BPS skyrmions in some BPS submodels of the generalized Skyrme model in five-dimensional spacetime using the BPS Lagrangian method. We focus on the static solutions of the Bogomolny’s equations and their corresponding energies with topological charge B > 0 is an integer. We consider two main cases based on the symmetry of the effective Lagrangian of the BPS submodels, i.e. the spherically symmetric and non-spherically symmetric cases. For the spherically symmetric case, we find two BPS submodels. The first BPS submodels consist of a potential term and a term proportional to the square of the topological current. The second BPS submodels consist of only the Skyrme term. The second BPS submodel has BPS skyrmions with the same topological charge B > 1, but with different energies, that we shall call “topological degenerate” BPS skyrmions. It also has the usual BPS skyrmions with equal energies, if the topological charge is a prime number. Another interesting feature of the BPS skyrmions, with B > 1, in this BPS submodel, is that these BPS skyrmions have non-zero pressures in the angular direction. For the non-spherically symmetric case, there is only one BPS submodel, which is similar to the first BPS submodel in the spherically symmetric case. We find that the BPS skyrmions depend on a constant k and for a particular value of k we obtain the BPS skyrmions of the first BPS submodel in the spherically symmetric case. The total static energy and the topological charge of these BPS skyrmions also depend on this constant. We also show that all the results found in this paper satisfy the full field equations of motions of the corresponding BPS submodels.

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Section: Jhep07(2021)090mentioning

confidence: 99%

Section: Jhep07(2021)090 3 Bps Skyrme Submodels In the Spherically Symmetric Lagrangian Densitymentioning

confidence: 99%

Section: Bps Skyrme Submodel In the Non-spherically Symmetric Lagrangian Densitymentioning

confidence: 99%

Section: Jhep07(2021)090mentioning

confidence: 99%

Section: Jhep07(2021)090 5 Conclusionmentioning

confidence: 99%

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BPS Skyrme submodels of the five-dimensional Skyrme model

Fadhilla

Gunara

Atmaja

2021

J. High Energ. Phys.

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BPS skyrmions of generalized Skyrme model in higher dimensions

Fadhilla

Atmaja

Gunara

2022

J. High Energ. Phys.

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In this work we consider the higher dimensional Skyrme model, with spatial dimension d > 3, focusing on its BPS submodels and their corresponding features. To accommodate the cases with a higher topological degree, B ≥ 1, a modified generalized hedgehog ansatz is used where we assign an integer ni for each rotational plane, resulting in a topological degree that proportional to product of these integers. It is found via BPS Lagrangian method that there are only two possible BPS submodels for this spherically symmetric ansatz which shall be called as BPS Skyrme model and scale-invariant model. The properties of the higher dimensional version of both submodels are studied and it is found that the BPS Skyrmions with B ≥ 1 exist in the first submodel but there is only B = 1 BPS Skyrmion in the second submodel. We also study the higher dimensional version of self-duality conditions in terms of strain tensor eigenvalues and find that, in general, the scale-invariant model has a stronger self-duality condition than the BPS Skyrme model.

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Comparison between the FOEL formalism and the BPS Lagrangian method in finding BPS equations of some models in various dimensions

Atmaja

2023

Proceedings of the 1st Conference on Quantum Sciences and Technology (Conquest 2022)

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BPS submodels of the generalized Skyrme model and how to find them

Cited by 8 publications

References 34 publications

BPS Skyrme submodels of the five-dimensional Skyrme model

BPS Skyrme submodels of the five-dimensional Skyrme model

BPS skyrmions of generalized Skyrme model in higher dimensions

Comparison between the FOEL formalism and the BPS Lagrangian method in finding BPS equations of some models in various dimensions

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