The moduli space of solutions to the Extended Bogomolny equations on $Σ\times \mathbb{R_+}$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916100172677120 |
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| author | Dimakis, Panagiotis |
| author_facet | Dimakis, Panagiotis |
| contents | We study moduli spaces of solutions to the extended Bogomolny equations on $Σ\times \mathbb{R_{+,y}}$ with gauge group $\operatorname{SL}(2,\mathbb{C})$ satisfying the generalized Nahm pole boundary condition as $y\to 0$ and limiting to complex flat connections as $y\to \infty$. Refining the Kobayashi-Hitchin correspondence of \cite{MH2}, we identify these moduli spaces with certain holomorphic lagrangian sub-manifolds inside the moduli space of Higgs bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10999 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The moduli space of solutions to the Extended Bogomolny equations on $Σ\times \mathbb{R_+}$ Dimakis, Panagiotis Differential Geometry Mathematical Physics We study moduli spaces of solutions to the extended Bogomolny equations on $Σ\times \mathbb{R_{+,y}}$ with gauge group $\operatorname{SL}(2,\mathbb{C})$ satisfying the generalized Nahm pole boundary condition as $y\to 0$ and limiting to complex flat connections as $y\to \infty$. Refining the Kobayashi-Hitchin correspondence of \cite{MH2}, we identify these moduli spaces with certain holomorphic lagrangian sub-manifolds inside the moduli space of Higgs bundles. |
| title | The moduli space of solutions to the Extended Bogomolny equations on $Σ\times \mathbb{R_+}$ |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2401.10999 |