Self-duality and the Holomorphic Ansatz in Generalized BPS Skyrme Model
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916824994545664 |
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| author | Ferreira, L. A. Livramento, L. R. |
| author_facet | Ferreira, L. A. Livramento, L. R. |
| contents | We propose a generalization of the BPS Skyrme model for simple compact Lie groups $G$ that leads to Hermitian symmetric spaces. In such a theory, the Skyrme field takes its values in $G$, while the remaining fields correspond to the entries of a symmetric, positive, and invertible $\dim G \times \dim G$-dimensional matrix $h$. We also use the holomorphic map ansatz between $S^2 \rightarrow G/H \times U(1)$ to study the self-dual sector of the theory, which generalizes the holomorphic ansatz between $S^2 \rightarrow CP^N$. This ansatz is constructed using the fact that stable harmonic maps of the two $S^2$ spheres for compact Hermitian symmetric spaces are holomorphic or anti-holomorphic. Apart from some special cases, the self-duality equations do not fix the matrix $h$ entirely in terms of the Skyrme field, which is completely free, as it happens in the original self-dual Skyrme model for $G=SU(2)$. In general, the freedom of the $h$ fields tend to grow with the dimension of $G$. The holomorphic ansatz enable us to construct an infinite number of exact self-dual Skyrmions for each integer value of the topological charge and for each value of $N \geq 1$, in case of the $CP^N$, and for each values of $p,\,q\geq 1$ in case of $SU(p+q)/SU(p)\otimes SU(q)\otimes U(1)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_11533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-duality and the Holomorphic Ansatz in Generalized BPS Skyrme Model Ferreira, L. A. Livramento, L. R. High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems We propose a generalization of the BPS Skyrme model for simple compact Lie groups $G$ that leads to Hermitian symmetric spaces. In such a theory, the Skyrme field takes its values in $G$, while the remaining fields correspond to the entries of a symmetric, positive, and invertible $\dim G \times \dim G$-dimensional matrix $h$. We also use the holomorphic map ansatz between $S^2 \rightarrow G/H \times U(1)$ to study the self-dual sector of the theory, which generalizes the holomorphic ansatz between $S^2 \rightarrow CP^N$. This ansatz is constructed using the fact that stable harmonic maps of the two $S^2$ spheres for compact Hermitian symmetric spaces are holomorphic or anti-holomorphic. Apart from some special cases, the self-duality equations do not fix the matrix $h$ entirely in terms of the Skyrme field, which is completely free, as it happens in the original self-dual Skyrme model for $G=SU(2)$. In general, the freedom of the $h$ fields tend to grow with the dimension of $G$. The holomorphic ansatz enable us to construct an infinite number of exact self-dual Skyrmions for each integer value of the topological charge and for each value of $N \geq 1$, in case of the $CP^N$, and for each values of $p,\,q\geq 1$ in case of $SU(p+q)/SU(p)\otimes SU(q)\otimes U(1)$. |
| title | Self-duality and the Holomorphic Ansatz in Generalized BPS Skyrme Model |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2504.11533 |