BPS Equations of Monopole and Dyon in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn fontstyle="italic">2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> Yang-Mills-Higgs Model, Nakamula-Shiraishi Models, and Their Generalized Versions from the BPS Lagrangian Method

Atmaja, Ardian Nata; Prasetyo, Ilham

doi:10.1155/2018/7376534

Cited by 6 publications

(23 citation statements)

References 24 publications

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“…The method not only succeeded in re-deriving the known BPS vortices, but it was also able to find new Bogomolny equations for other BPS vortices [24]. 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].…”

Section: Jhep07(2021)090mentioning

confidence: 99%

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%

BPS Skyrme submodels of the five-dimensional Skyrme model

Fadhilla

Gunara

Atmaja

2021

J. High Energ. Phys.

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“…These solutions turn out to be solutions of first-order differential equations, known as Bogomolny's equations, that were derived by Bogomolny [10]. 1 The solutions saturate the non-trivial static energy bound which turns out to be proportional with the topological charge. Obtaining the Bogomolny's equations of a model is important in particular to study the topological stability of its solitons solutions.…”

Section: Introductionmentioning

confidence: 99%

“…These Bogomolny's equations exist only if the scalar fieldsdependent couplings are related to each other by an equation. On the other hand, the BPS Lagrangian method has been used to rederive the Bogomolny's equations for BPS monopoles and it also managed to obtain the Bogomolny's equations for BPS dyons, which exist only if the scalar fieldsdependent couplings are related to each other by a more general equation [1]. However, all those derivations rely on a particular hedgehog ansatz namely 't Hooft-Polyakov and Julia-Zee ansatze for monopoles and dyons respectively.…”

Section: Introductionmentioning

confidence: 99%

“…It is then necessary to find the generalized Bogomolny's equations for BPS monopoles and dyons in general coordinate system that are independent of any ansatz in order to study other possible soliton solutions and configurations. We also would like to verify if the relations between scalar fieldsdependent couplings for BPS monopoles and dyons, derived in [1] for the Julia-Zee ansatz, are still hold in the general coordinate system for any ansatz. Nevertheless the existence of these Bogomolny's equations in general coordinate system are inevitable for extending the corresponding model to its supersymmetric version.…”

Section: Introductionmentioning

confidence: 99%

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Are there BPS dyons in the generalized SU(2) Yang–Mills–Higgs model?

Atmaja

2022

Eur. Phys. J. C

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We use the well-known Bogomolny’s equations, in general coordinate system, for BPS monopoles and dyons in the SU(2) Yang–Mills–Higgs model to obtain an explicit form of BPS Lagrangian density under the BPS Lagrangian method. We then generalize this BPS Lagrangian density and use it to derive several possible generalized Bogomolny’s equations, with(out) additional constraint equations, for BPS monopoles and dyons in the generalized SU(2) Yang–Mills–Higgs model. We also compute the stress–energy–momentum tensor of the generalized model, and argue that the BPS monopole and dyon solutions are stable if all components of the stress-tensor density are zero in the BPS limit. This stability requirement implies the scalar fields-dependent couplings to be related to each other by an equation, which is different from the one obtained in Atmaja and Prasetyo (Adv High Energy Phys 2018:7376534, arXiv: 1803.06122, 2018), and then picks particular generalized Bogomolny’s equations, with no additional constraint equation, out of those possible equations. We show that the computations in [1] are actually incomplete. Under the Julia–Zee ansatz, the generalized Bogomolny’s equations imply all scalar fields-dependent couplings must be constants, whose solutions are the BPS dyons of the SU(2) Yang–Mills–Higgs model (Prasad and Sommerfield in Phys Rev Lett 35:760, 1975), or in another words there are no generalized BPS dyon solutions under the Julia–Zee ansatz. We propose two possible ways for obtaining generalized BPS dyons, where at least one of the scalar fields-dependent couplings is not constant, that are by using different ansatze, such as axially symmetric ansatz for higher topological charge dyons; and/or by considering the most general BPS Lagrangian density.

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“…While Lattice QCD (LQCD) provides the most direct approach for studying high-temperature systems [1,2], it is plagued by the familiar fermion sign-problem [3,4,5,6,7,8,9] at non-vanishing baryo-chemical potentials. Effective Lagrangian models [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31], on the other hand, provide a much more tractable alternative to the study of non-perturbative, strongly-interacting matter. Following this approach, in Ref.…”

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confidence: 99%

Effects of a non-zero strangeness-chemical potential in strong interaction models

2019

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The effect of a non-zero strangeness chemical potential on the strong interaction phase diagram has been studied within the framework of the SU(3) quark-hadron chiral parity-doublet model. Both, the nuclear liquid-gas and the chiral/deconfinement phase transitions are modified. The first-order line in the chiral phase transition is observed to vanish completely, with the entire phase boundary becoming a crossover. These changes in the nature of the phase transitions are expected to modify various susceptibilities, the effects of which might be detectable in particle-number distributions resulting from moderate-temperature and high-density heavy-ion collision experiments.

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BPS Equations of Monopole and Dyon in SU(2) Yang-Mills-Higgs Model, Nakamula-Shiraishi Models, and Their Generalized Versions from the BPS Lagrangian Method

Cited by 6 publications

References 24 publications

BPS Skyrme submodels of the five-dimensional Skyrme model

BPS Skyrme submodels of the five-dimensional Skyrme model

Are there BPS dyons in the generalized SU(2) Yang–Mills–Higgs model?

Effects of a non-zero strangeness-chemical potential in strong interaction models

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