Nahm gauge fields for the torus

TL;DR

This paper derives an exact expression for Nahm gauge fields related to self-dual gauge fields on a four-dimensional space with a three-torus and real line, revealing how instanton size relates to boundary conditions.

Contribution

It provides the first explicit formula for Nahm gauge fields in this setting, linking instanton size to boundary flat connections.

Findings

Exact expression for Nahm gauge fields on T^3 x R.

Instanton size determined by boundary flat connections.

Connection between gauge field properties and boundary conditions.

Abstract

We present the exact expression for the Nahm gauge field associated to a SU(N) charge one self-dual gauge field on T^3XR. The result implies that the size of the instanton is determined by the ``distance'' between its two flat connections at t plus or minus infinty.