Are there BPS dyons in the generalized SU(2) Yang–Mills–Higgs model?
Abstract 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 deriv...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-07-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-022-10569-6 |
| _version_ | 1818158419318669312 |
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| author | Ardian Nata Atmaja |
| author_facet | Ardian Nata Atmaja |
| author_sort | Ardian Nata Atmaja |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-11T15:29:47Z |
| format | Article |
| id | doaj.art-0599918a7f484b538334bbe53d312291 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-12-11T15:29:47Z |
| publishDate | 2022-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-0599918a7f484b538334bbe53d3122912022-12-22T01:00:05ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522022-07-0182711310.1140/epjc/s10052-022-10569-6Are there BPS dyons in the generalized SU(2) Yang–Mills–Higgs model?Ardian Nata Atmaja0Research Center for Quantum Physics, National Research and Innovation Agency (BRIN)Abstract 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.https://doi.org/10.1140/epjc/s10052-022-10569-6 |
| spellingShingle | Ardian Nata Atmaja Are there BPS dyons in the generalized SU(2) Yang–Mills–Higgs model? European Physical Journal C: Particles and Fields |
| title | Are there BPS dyons in the generalized SU(2) Yang–Mills–Higgs model? |
| title_full | Are there BPS dyons in the generalized SU(2) Yang–Mills–Higgs model? |
| title_fullStr | Are there BPS dyons in the generalized SU(2) Yang–Mills–Higgs model? |
| title_full_unstemmed | Are there BPS dyons in the generalized SU(2) Yang–Mills–Higgs model? |
| title_short | Are there BPS dyons in the generalized SU(2) Yang–Mills–Higgs model? |
| title_sort | are there bps dyons in the generalized su 2 yang mills higgs model |
| url | https://doi.org/10.1140/epjc/s10052-022-10569-6 |
| work_keys_str_mv | AT ardiannataatmaja aretherebpsdyonsinthegeneralizedsu2yangmillshiggsmodel |