Adiabatic dynamics of instantons on $S ^4 $

Guido Franchetti; Bernd J. Schroers

doi:10.1007/s00220-016-2769-6

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arXiv · 1508.06566

Adiabatic dynamics of instantons on $S ^4 $

Guido Franchetti·Bernd J. Schroers

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Abstract

We define and compute the $L^2$ metric on the framed moduli space of circle invariant 1-instantons on the 4-sphere. This moduli space is four dimensional and our metric is $SO(3) \times U(1)$ symmetric. We study the behaviour of generic geodesics and show that the metric is geodesically incomplete. Circle-invariant instantons on the 4-sphere can also be viewed as hyperbolic monopoles, and we interpret our results from this viewpoint. We relate our results to work by Habermann on unframed instantons on the 4-sphere and, in the limit where the radius of the 4-sphere tends to infinity, to results on instantons on Euclidean 4-space.

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Guido Franchetti, Bernd J. Schroers. 2016-06-22. Adiabatic dynamics of instantons on $S ^4 $. https://doi.org/10.1007/s00220-016-2769-6

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