ADHM Revisited: Instantons and Wilson Lines

TL;DR

This work connects the ADHM construction of self-dual gauge fields to D-brane dynamics by introducing a Wilson line into the D0-D4 system. It shows that the Wilson line induces a Lorentz-like force on moving instantons, captured by a U(N) connection Omega over the instanton moduli space M_{k,N}, and that the D0-brane quantum mechanics reproduces the ADHM data for the gauge field. The framework extends ADHM to dynamical settings with impurity degrees of freedom and yields a N=(0,4) supersymmetric quantum mechanics that encodes the full gauge connection. The results deepen the link between soliton dynamics in gauge theory and the ADHM construction, with potential implications for impurity dynamics in field theory and string theory.

Abstract

We revisit the well-studied D0-D4 system of D-branes and its relationship to the ADHM construction. It is well known that the D0-branes appear as instantons in the D4-brane worldvolume. We add a Wilson line to the D4-brane in the guise of an extended fundamental string and determine how this affects the D0-brane dynamics. As the D0-brane moves in the presence of the Wilson line, it experiences a Lorentz force, proportional to its Yang-Mills gauge connection. From the perspective of the D0-brane quantum mechanics, this force emerges through the ADHM construction of the self-dual gauge connection.