Adiabatic Dynamics of Instantons on S4

Guido Franchetti, Bernd Johannes Schroers

Research output: Contribution to journalArticle

1 Citation (Scopus)
19 Downloads (Pure)

Abstract

We define and compute the L2 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 (Formula presented.) 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.

Original languageEnglish
Pages (from-to)185–228
Number of pages44
JournalCommunications in Mathematical Physics
Volume353
Issue number1
Early online date15 Oct 2016
DOIs
Publication statusPublished - Jul 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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