BPS Skyrme models and contact geometry
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913578179624960 |
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| author | Slobodeanu, Radu Speight, Martin |
| author_facet | Slobodeanu, Radu Speight, Martin |
| contents | A Skyrme type energy functional for maps $φ$ from an oriented Riemannian 3-manifold $M$ to a contact 3-manifold $N$ is defined, generalizing the BPS Skyrme energy of Ferreira and Zakrzewski. This energy has a topological lower bound, attained by solutions of a first order self-duality equation which we call (strong) Beltrami maps. In the case where $N$ is the 3-sphere, we show that the original Ferreira-Zakrzewski model (which has $N=S^3$ with the standard contact structure) can have no BPS solutions on $M=S^3$ with $|\mathrm{deg}(φ)|>1$ if the coupling constant has the lowest admissible value. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_09649 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | BPS Skyrme models and contact geometry Slobodeanu, Radu Speight, Martin Differential Geometry High Energy Physics - Theory Mathematical Physics A Skyrme type energy functional for maps $φ$ from an oriented Riemannian 3-manifold $M$ to a contact 3-manifold $N$ is defined, generalizing the BPS Skyrme energy of Ferreira and Zakrzewski. This energy has a topological lower bound, attained by solutions of a first order self-duality equation which we call (strong) Beltrami maps. In the case where $N$ is the 3-sphere, we show that the original Ferreira-Zakrzewski model (which has $N=S^3$ with the standard contact structure) can have no BPS solutions on $M=S^3$ with $|\mathrm{deg}(φ)|>1$ if the coupling constant has the lowest admissible value. |
| title | BPS Skyrme models and contact geometry |
| topic | Differential Geometry High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2411.09649 |