Geometry of the tt*-Toda equations I: universal centralizer and symplectic groupoids
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arXiv
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| Format: | Preprint |
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2026
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| author | Guest, Martin A. Ho, Nan-Kuo |
| author_facet | Guest, Martin A. Ho, Nan-Kuo |
| contents | We investigate the geometry of a certain space of meromorphic connections with irregular singularities, and prove in particular that it is a (real) symplectic Lie groupoid. The connections have a physical meaning: they correspond to certain solutions of the topological-antitopological fusion (tt*) equations of Cecotti and Vafa, and hence to deformations of supersymmetric quantum field theories. The groupoid structure arises because we restrict ourselves to the tt* equations of Toda type, whose monodromy data has a Lie theoretic description. To obtain these results, we show first that the universal centralizer of a Lie group is a holomorphic symplectic groupoid over the Steinberg cross section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04358 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometry of the tt*-Toda equations I: universal centralizer and symplectic groupoids Guest, Martin A. Ho, Nan-Kuo Symplectic Geometry High Energy Physics - Theory Differential Geometry Primary 53D05, 34M40, Secondary 22E10, 53C43, 81T40 We investigate the geometry of a certain space of meromorphic connections with irregular singularities, and prove in particular that it is a (real) symplectic Lie groupoid. The connections have a physical meaning: they correspond to certain solutions of the topological-antitopological fusion (tt*) equations of Cecotti and Vafa, and hence to deformations of supersymmetric quantum field theories. The groupoid structure arises because we restrict ourselves to the tt* equations of Toda type, whose monodromy data has a Lie theoretic description. To obtain these results, we show first that the universal centralizer of a Lie group is a holomorphic symplectic groupoid over the Steinberg cross section. |
| title | Geometry of the tt*-Toda equations I: universal centralizer and symplectic groupoids |
| topic | Symplectic Geometry High Energy Physics - Theory Differential Geometry Primary 53D05, 34M40, Secondary 22E10, 53C43, 81T40 |
| url | https://arxiv.org/abs/2604.04358 |