Special Kähler geometries of $\mathcal{N}=4$ superYang-Mills
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918158505345024 |
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| author | Argyres, Philip C. Bourget, Antoine Grimminger, Julius F. Lotito, Matteo Weaver, Mitch |
| author_facet | Argyres, Philip C. Bourget, Antoine Grimminger, Julius F. Lotito, Matteo Weaver, Mitch |
| contents | The low energy effective theory on the moduli space of vacua of 4d superYang-Mills (sYM) theory defines a special Kähler geometry. For simple sYM gauge algebras, $\mathfrak{g}$, we classify all compatible special Kähler structures by showing that they are in one-to-one correspondence with certain equivalence classes of integral symplectic representations of the Weyl group of $\mathfrak{g}$. We further demonstrate that, for principal Dirac pairing, these equivalence classes are in one-to-one correspondence with the S-duality orbits of the global structures of the corresponding $\mathfrak{g}$ sYM gauge theory, after a mistake in the field theory literature is corrected. This provides a low-energy test of S-duality. We also discuss twisted product geometries made from factors with special Kähler structures with non-principal Dirac pairings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Special Kähler geometries of $\mathcal{N}=4$ superYang-Mills Argyres, Philip C. Bourget, Antoine Grimminger, Julius F. Lotito, Matteo Weaver, Mitch High Energy Physics - Theory The low energy effective theory on the moduli space of vacua of 4d superYang-Mills (sYM) theory defines a special Kähler geometry. For simple sYM gauge algebras, $\mathfrak{g}$, we classify all compatible special Kähler structures by showing that they are in one-to-one correspondence with certain equivalence classes of integral symplectic representations of the Weyl group of $\mathfrak{g}$. We further demonstrate that, for principal Dirac pairing, these equivalence classes are in one-to-one correspondence with the S-duality orbits of the global structures of the corresponding $\mathfrak{g}$ sYM gauge theory, after a mistake in the field theory literature is corrected. This provides a low-energy test of S-duality. We also discuss twisted product geometries made from factors with special Kähler structures with non-principal Dirac pairings. |
| title | Special Kähler geometries of $\mathcal{N}=4$ superYang-Mills |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.02057 |