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Adiabatic Dynamics of Instantons on S 4

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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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Authors and Affiliations

  1. Institut für Theoretische Physik, Leibniz Universität, Hannover, Germany

    Guido Franchetti

  2. Maxwell Institute for Mathematical Sciences and Department of Mathematics, Heriot-Watt University, Edinburgh, UK

    Bernd J. Schroers

Authors
  1. Guido Franchetti
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  2. Bernd J. Schroers
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Correspondence to Guido Franchetti.

Additional information

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

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