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Singular Instantons and Painlevé VI
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Singular Instantons and Painlevé VI
Інший ID:
2010 Mathematics Subject Classification: 34M55; 53C07; 53C28
DOI:10.3842/SIGMA.2016.057
DOI:10.3842/SIGMA.2016.057
Посилання:
Singular Instantons and Painlevé VI / R. Muñiz Manasliski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 24 назв. — англ.
Підтримка:
s
The author would like to thank Nigel Hitchin for his suggestion to look at instantons with
holonomic singularities and Gil Bor for many useful conversations. We also thank the referees
for many useful suggestions that help to improve the paper. This work was partially supported
by Grupo CSIC 618 (UdelaR, Uruguay).
Дата:
2016
Переглядів:
425
Завантажень:
175
Анотація:
We consider a two parameter family of instantons, which is studied in [Sadun L., Comm. Math. Phys. 163 (1994), 257-291], invariant under the irreducible action of SU₂ on S⁴, but which are not globally defined. We will see that these instantons produce solutions to a one parameter family of Painlevé VI equations (PVI) and we will give an explicit expression of the map between instantons and solutions to PVI. The solutions are algebraic only for that values of the parameters which correspond to the instantons that can be extended to all of S⁴. This work is a generalization of [Muñiz Manasliski R., Contemp. Math., Vol. 434, Amer. Math. Soc., Providence, RI, 2007, 215-222] and [Muñiz Manasliski R., J. Geom. Phys. 59 (2009), 1036-1047, arXiv:1602.07221], where instantons without singularities are studied.
