Interpreting the Ooguri-Vafa symplectic form à la Atiyah-Bott
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912819018989568 |
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| author | Nackan, Danny |
| author_facet | Nackan, Danny |
| contents | Gaiotto, Moore, and Neitzke predicted that the hyperkähler Ooguri-Vafa space $\mathcal{M}^{\rm ov}$ should provide a local model for Hitchin moduli spaces near the discriminant locus. To this end, Tulli identified $\mathcal{M}^{\rm ov}$ with a certain space of framed Higgs bundles with an irregular singularity. We extend this result by identifying the Ooguri-Vafa holomorphic symplectic form with a regularized version of the Atiyah-Bott form on the associated space of framed connections. We also prove the analogous statement for the corresponding semiflat forms. Finally, restricting to the Hitchin section, we identify a regularized version of Hitchin's $L^2$-metric with the Ooguri-Vafa metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19789 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interpreting the Ooguri-Vafa symplectic form à la Atiyah-Bott Nackan, Danny Differential Geometry High Energy Physics - Theory Algebraic Geometry Gaiotto, Moore, and Neitzke predicted that the hyperkähler Ooguri-Vafa space $\mathcal{M}^{\rm ov}$ should provide a local model for Hitchin moduli spaces near the discriminant locus. To this end, Tulli identified $\mathcal{M}^{\rm ov}$ with a certain space of framed Higgs bundles with an irregular singularity. We extend this result by identifying the Ooguri-Vafa holomorphic symplectic form with a regularized version of the Atiyah-Bott form on the associated space of framed connections. We also prove the analogous statement for the corresponding semiflat forms. Finally, restricting to the Hitchin section, we identify a regularized version of Hitchin's $L^2$-metric with the Ooguri-Vafa metric. |
| title | Interpreting the Ooguri-Vafa symplectic form à la Atiyah-Bott |
| topic | Differential Geometry High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2409.19789 |