Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 1

Monads for instantons and bows

Pages: 167 – 251



Sergey A. Cherkis (Department of Mathematics, University of Arizona, Tucson, Az., U.S.A.)

Jacques Hurtubise (Department of Mathematics, McGill University, Montréal, Québec, Canada)


Instantons on the Taub-NUT space are related to ‘bow solutions’ via a generalization of the ADHM-Nahm transform. Both are related to complex geometry, either via the twistor transform or via the Kobayashi–Hitchin correspondence. We explore various aspects of this complex geometry, exhibiting equivalences. For both the instanton and the bow solution we produce two monads encoding each of them respectively. Identifying these monads we establish the one-to-one correspondence between the instanton and the bow solution.

The work of SCh was partially supported by the Simons Foundation grant #245643, and that of JH by NSERC grant # RGPIN-2015-04393. The authors are grateful to the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Metric and Analytic Aspects of Moduli Spaces where part of the work on this paper was undertaken, supported by EPSRC grant no EP/K032208/1. SCh thanks the Berkeley Center for Theoretical Physics for hospitality during the final stages of this work. The authors also thank the Banff International Research Station for hospitality during the workshop The Analysis of Gauge-Theoretic Moduli Spaces where this work was completed.

Published 27 September 2019