Isomonodromic deformations and SU2-invariant instantons on S4
arXiv:1602.07221 · doi:10.1016/j.geomphys.2009.04.009
Abstract
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 C P 1 having four simple singularities. As is well known this kind of deformations is governed by the sixth Painlevé equation P vi (α, \b{eta}, 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 pa- rameters (α, \b{eta}, γ, δ) in terms of the instanton number. The present paper contains the proof of the result anounced in [16].