Blowup relations and $q$-Painlevé VI
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911203419226112 |
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| author | Stoyan, Artem |
| author_facet | Stoyan, Artem |
| contents | We propose and study blowup relations obeyed by the partition functions of $5d$ $\mathcal{N}=1$ (quiver) SYM theories with $SU(2)$ gauge group and four flavours. By analyzing the Weyl group action on the sets of blowup relations, we identify the integer parameters of a blowup relation with the weights of a corresponding Lie algebra. We also explain how this action of the Weyl group follows from the Weyl group symmetry of the partition function. Finally, we use these relations to derive bilinear relations on the $q$-Painlevé VI tau functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blowup relations and $q$-Painlevé VI Stoyan, Artem Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems We propose and study blowup relations obeyed by the partition functions of $5d$ $\mathcal{N}=1$ (quiver) SYM theories with $SU(2)$ gauge group and four flavours. By analyzing the Weyl group action on the sets of blowup relations, we identify the integer parameters of a blowup relation with the weights of a corresponding Lie algebra. We also explain how this action of the Weyl group follows from the Weyl group symmetry of the partition function. Finally, we use these relations to derive bilinear relations on the $q$-Painlevé VI tau functions. |
| title | Blowup relations and $q$-Painlevé VI |
| topic | Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2509.10938 |