Constituent monopoles through the eyes of fermion zero-modes

TL;DR

This paper investigates the structure of constituent monopoles in multi-caloron solutions using fermion zero-modes, revealing extended structures that become point-like when constituents are well separated, with exact solutions for SU(2) charge 2 cases.

Contribution

It provides an exact analysis of fermion zero-modes in multi-caloron backgrounds, especially solving the Nahm equation for SU(2) charge 2 solutions beyond previous approximations.

Findings

Zero-mode density indicates extended structures for overlapping constituents.

Well-separated constituents appear point-like in zero-mode density.

Exact solutions relate zero-mode density to conserved Nahm quantities.

Abstract

We use the fermion zero-modes in the background of multi-caloron solutions with non-trivial holonomy as a probe for constituent monopoles. We find in general indication for an extended structure. However, for well separated constituents these become point-like. We analyse this in detail for the SU(2) charge 2 case, where one is able to solve the relevant Nahm equation exactly, beyond the piecewize constant solutions studied previously. Remarkably the zero-mode density can be expressed in the high temperature limit as a function of the conserved quantities that classify the solutions of the Nahm equation.