Blowups in BPS/CFT correspondence, and Painlevé VI
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arXiv
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| Formato: | Preprint |
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2020
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| _version_ | 1866929646580269056 |
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| author | Nekrasov, Nikita |
| author_facet | Nekrasov, Nikita |
| contents | We study four dimensional supersymmetric gauge theory in the presence of surface and point-like defects (blowups) and propose an identity relating partition functions at different values of $Ω$-deformation parameters $({\varepsilon}_{1}, {\varepsilon}_{2})$. As a consequence, we obtain the formula conjectured in 2012 by O$.$Gamayun, N$.$Iorgov, and O$.$Lysovyy, relating the tau-function $τ_{PVI}$ to $c=1$ conformal blocks of Liouville theory and propose its generalization for the case of Garnier-Schlesinger system. To this end we clarify the notion of the quasiclassical tau-function $τ_{PVI}$ of Painlevé VI and its generalizations. We also make some remarks about the sphere partition functions, the boundary operator product expansion in the ${\mathcal{N}}=(4,4)$ sigma models related to four dimensional ${\mathcal{N}}=2$ theories on toric manifolds, discuss crossed instantons on conifolds, elucidate some aspects of the BPZ/KZ correspondence, and applications to quantization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_03646 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Blowups in BPS/CFT correspondence, and Painlevé VI Nekrasov, Nikita High Energy Physics - Theory Mathematical Physics Combinatorics Differential Geometry 05A15, 05A17, 81T13, 81T35, 53C07 We study four dimensional supersymmetric gauge theory in the presence of surface and point-like defects (blowups) and propose an identity relating partition functions at different values of $Ω$-deformation parameters $({\varepsilon}_{1}, {\varepsilon}_{2})$. As a consequence, we obtain the formula conjectured in 2012 by O$.$Gamayun, N$.$Iorgov, and O$.$Lysovyy, relating the tau-function $τ_{PVI}$ to $c=1$ conformal blocks of Liouville theory and propose its generalization for the case of Garnier-Schlesinger system. To this end we clarify the notion of the quasiclassical tau-function $τ_{PVI}$ of Painlevé VI and its generalizations. We also make some remarks about the sphere partition functions, the boundary operator product expansion in the ${\mathcal{N}}=(4,4)$ sigma models related to four dimensional ${\mathcal{N}}=2$ theories on toric manifolds, discuss crossed instantons on conifolds, elucidate some aspects of the BPZ/KZ correspondence, and applications to quantization. |
| title | Blowups in BPS/CFT correspondence, and Painlevé VI |
| topic | High Energy Physics - Theory Mathematical Physics Combinatorics Differential Geometry 05A15, 05A17, 81T13, 81T35, 53C07 |
| url | https://arxiv.org/abs/2007.03646 |