Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 041, 11 pages      arXiv:2208.14936      https://doi.org/10.3842/SIGMA.2023.041
Contribution to the Special Issue on Topological Solitons as Particles

Deformations of Instanton Metrics

Roger Bielawski ^a, Yannic Borchard ^a and Sergey A. Cherkis ^b
a) Institut für Differentialgeometrie, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
^b) Department of Mathematics, The University of Arizona, 617 N. Santa Rita Ave., Tucson, AZ 85721-0089, USA

Received January 25, 2023, in final form June 05, 2023; Published online June 13, 2023

Abstract
We discuss a class of bow varieties which can be viewed as Taub-NUT deformations of moduli spaces of instantons on noncommutative $\mathbb R^4$. Via the generalized Legendre transform, we find the Kähler potential on each of these spaces.

Key words: instanton; bow variety; hyperkähler geometry; generalised Legendre transform.

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