Symmetric instantons and the ADHM construction

Bor, Gil; Segert, Jan

doi:10.1007/bf02509801

Cited by 5 publications

(23 citation statements)

References 21 publications

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“…But using an equivariant version of the ADHM construction one can obtain the following statement [18]: And these vector bundles are just what we needed in order to apply the general construction mentioned in Section 2, since as we have seen, the lines in the family P t intersect the divisor at four different points for t ∈ (0, 1), and then the hypotheses of Proposition 2.4 are satisfied.…”

Section: Description Of the Invariant Instantons Over Smentioning

confidence: 95%

Isomonodromic deformations and SU2-invariant instantons on S4

Manasliski

2009

Journal of Geometry and Physics

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a b s t r a c tAnti-self-dual (ASD) solutions to the Yang-Mills equation (or instantons) over an antiself-dual 4-manifold, which are invariant under an appropriate action of a threedimensional Lie group, give rise, via twistor construction, to isomonodromic deformations of connections on CP 1 having four simple singularities. As is well known, such deformations are governed by the sixth Painlevé equation Pvi (α, β, γ , δ). We work out the particular case of the SU 2 -action on S 4 , obtained from the irreducible representation on R 5 . In particular, we express the parameters (α, β, γ , δ) in terms of the instanton number. The present paper contains the proof of the result announced in [Richard Muñiz Manasliski, Painlevé VI equation from invariant instantons, in: Geometric and Topological Methods for

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Section: Description Of the Invariant Instantons Over Smentioning

confidence: 95%

Isomonodromic deformations and SU2-invariant instantons on S4

Manasliski

2009

Journal of Geometry and Physics

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“…For the existence of ASD connections (without any singularity) the weight of RP + has to be equal to one. Let us denote by E n the equivariant vector bundle whose weights are n on RP − and 1 on RP + [5].…”

Section: )mentioning

confidence: 99%

Singular Instantons and Painlevé VI

Manasliski¹

2016

SIGMA

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Abstract. 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 SU 2 on S 4 , but which are not globally defined. We will see that these instantons produce solutions to a one parameter family of Painlevé VI equations (P VI ) and we will give an explicit expression of the map between instantons and solutions to P VI . The solutions are algebraic only for that values of the parameters which correspond to the instantons that can be extended to all of S 4 . This work is a generalization of [Muñiz Manasliski R

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“…It is possible to prove that those vector bundles for which n + > 1 and n − > 1 do not admit any self-dual or anti-self-dual SU 2 -invariant connection ( [4]). But using an equivariant version of the ADHM construction one can obtain the following statement [6]:…”

Section: 2mentioning

confidence: 99%

Isomonodromic deformations and SU2-invariant instantons on S4

Manasliski

2016

Preprint

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Anti-self-dual (ASD) solutions to the Yang-Mills equation (or instantons) over an anti-self-dual four manifold, which are invariant under an appropriate action of a three dimensional Lie group, give rise, via twistor construction, to isomonodromic deformations of connections on CP 1 having four simple singularities. As is well known this kind of deformations is governed by the sixth Painlevé equation Pvi(α, β, γ, δ). We work out the particular case of the SU2-action on S 4 , obtained from the irreducible representation on R 5 . In particular, we express the parameters (α, β, γ, δ) in terms of the instanton number. The present paper contains the proof of the result anounced in [16].

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Symmetric instantons and the ADHM construction

Cited by 5 publications

References 21 publications

Isomonodromic deformations and SU2-invariant instantons on S4

Isomonodromic deformations and SU2-invariant instantons on S4

Singular Instantons and Painlevé VI

Isomonodromic deformations and SU2-invariant instantons on S4

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