One-parameter family of selfdual solutions in classical Yang-Mills theory

TL;DR

This paper introduces a new family of selfdual solutions in SU(2) Yang-Mills theory derived via an l^2 vector space extension of the ADHM construction, connecting to monopole solutions as a parameter varies.

Contribution

It extends the ADHM construction to an infinite-dimensional setting, creating a one-parameter family of solutions that generalize known monopole configurations.

Findings

A continuous family of selfdual solutions parameterized by q.

The solutions interpolate between known monopole configurations and other selfdual solutions.

The formulation acts as a q-analog of Nahm's monopole construction.

Abstract

The ADHM construction, which yields (anti-)selfdual configurations in classical Yang-Mills theories, is applied to an infinite dimensional l^2 vector space, and as a consequence, a family of (anti-)selfdual configurations with a parameter q is obtained for SU(2) Yang-Mills theory. This l^2 formulation can be seen as a q-analog of Nahm's monopole construction, so that the configuration approaches the BPS monopole at q->1 limit.