Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2017
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1705.01869 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918281594535936 |
|---|---|
| author | Gavrylenko, P. Lisovyy, O. |
| author_facet | Gavrylenko, P. Lisovyy, O. |
| contents | We show that the dual partition function of the pure $\mathcal N=2$ $SU(2)$ gauge theory in the self-dual $Ω$-background (a) is given by Fredholm determinant of a generalized Bessel kernel and (b) coincides with the tau function associated to the general solution of the Painlevé III equation of type $D_8$ (radial sine-Gordon equation). In particular, the principal minor expansion of the Fredholm determinant yields Nekrasov combinatorial sums over pairs of Young diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1705_01869 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Pure $SU(2)$ gauge theory partition function and generalized Bessel kernel Gavrylenko, P. Lisovyy, O. Mathematical Physics High Energy Physics - Theory We show that the dual partition function of the pure $\mathcal N=2$ $SU(2)$ gauge theory in the self-dual $Ω$-background (a) is given by Fredholm determinant of a generalized Bessel kernel and (b) coincides with the tau function associated to the general solution of the Painlevé III equation of type $D_8$ (radial sine-Gordon equation). In particular, the principal minor expansion of the Fredholm determinant yields Nekrasov combinatorial sums over pairs of Young diagrams. |
| title | Pure $SU(2)$ gauge theory partition function and generalized Bessel kernel |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/1705.01869 |