A q-analog of the ADHMN construction and axisymmetric multi-instantons

TL;DR

This paper introduces a q-analog of the ADHMN construction, generating a family of anti-selfdual solutions in SU(2) Yang-Mills theory, linking q-analysis functions with axisymmetric ansatz solutions.

Contribution

It develops a novel q-analog framework for the ADHMN construction, extending the understanding of anti-selfdual configurations in Yang-Mills theory.

Findings

Introduces a q-analog of the ADHMN construction.

Connects q-exponential functions with axisymmetric anti-selfdual solutions.

Provides a new perspective on monopole solutions via q-analysis.

Abstract

In the preceding paper (Phys. Lett. B463 (1999) 257), the authors presented a q-analog of the ADHMN construction and obtained a family of anti-selfdual configurations with a parameter q for classical SU(2) Yang-Mills theory in four-dimensional Euclidean space. The family of solutions can be seen as a q-analog of the single BPS monopole preserving (anti-)selfduality. Further discussion is made on the relation to axisymmetric ansatz on anti-selfdual equation given by Witten in the late seventies. It is found that the q-exponential functions familiar in q-analysis appear as analytic functions categorizing the anti-selfdual configurations yielded by axisymmetric ansatz.