Constituents of Doubly Periodic Instantons

TL;DR

This paper uses the Nahm transform to analyze doubly periodic SU(2) instantons with radial symmetry, identifying constituent locations and computing action densities to understand their structure.

Contribution

It introduces a detailed analysis of doubly periodic instantons, identifying constituent points and providing analytical and numerical action density computations.

Findings

Identified special points as constituent locations.

Computed action density analytically and numerically.

Showed that cutting the torus yields twisted charge 1/2 instantons.

Abstract

Using the Nahm transform we investigate doubly periodic charge one SU(2) instantons with radial symmetry. Two special points where the Nahm zero modes have softer singularities are identified as constituent locations. To support this picture, the action density is computed analytically and numerically within a two dimensional slice containing the two constituents. For particular values of the parameters the torus can be cut in half yielding two copies of a twisted charge 1/2 instanton. Such objects comprise a single constituent.