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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Communicated by N. A. Nekrasov
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Franchetti, G., Schroers, B.J. Adiabatic Dynamics of Instantons on S 4 . Commun. Math. Phys. 353, 185–228 (2017). https://doi.org/10.1007/s00220-016-2769-6
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DOI: https://doi.org/10.1007/s00220-016-2769-6