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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.17198 |
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| _version_ | 1866917378789474304 |
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| author | Yoshida, Yutaka |
| author_facet | Yoshida, Yutaka |
| contents | We show that transformation formulas of multiple $q$-hypergeometric series agree with wall-crossing formulas of $K$-theoretic vortex partition functions obtained by Hwang, Yi and the author \cite{Hwang:2017kmk}. For the vortex partition function in 3d $\mathcal{N}=2$ gauge theory, we show that the wall-crossing formula agrees with the Kajihara transformation \cite{kajihara2004euler}. For the vortex partition function in 3d $\mathcal{N}=4$ gauge theory, we show that the wall-crossing formula agrees with the transformation formula by Hallnäs, Langmann, Noumi and Rosengren \cite{Halln_s_2022}. Since the $K$-theoretic vortex partition functions are related with indices such as the $χ_t$-genus of the handsaw quiver variety, we discuss geometric interpretation of Euler transformations in terms of wall-crossing formulas of handsaw quiver variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Euler transformation for multiple $q$-hypergeometric series from wall-crossing formula of $K$-theoretic vortex partition function Yoshida, Yutaka High Energy Physics - Theory Mathematical Physics Algebraic Geometry We show that transformation formulas of multiple $q$-hypergeometric series agree with wall-crossing formulas of $K$-theoretic vortex partition functions obtained by Hwang, Yi and the author \cite{Hwang:2017kmk}. For the vortex partition function in 3d $\mathcal{N}=2$ gauge theory, we show that the wall-crossing formula agrees with the Kajihara transformation \cite{kajihara2004euler}. For the vortex partition function in 3d $\mathcal{N}=4$ gauge theory, we show that the wall-crossing formula agrees with the transformation formula by Hallnäs, Langmann, Noumi and Rosengren \cite{Halln_s_2022}. Since the $K$-theoretic vortex partition functions are related with indices such as the $χ_t$-genus of the handsaw quiver variety, we discuss geometric interpretation of Euler transformations in terms of wall-crossing formulas of handsaw quiver variety. |
| title | Euler transformation for multiple $q$-hypergeometric series from wall-crossing formula of $K$-theoretic vortex partition function |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2401.17198 |