Multi-Caloron solutions

TL;DR

This paper constructs and analyzes multi-caloron solutions with non-trivial holonomy, providing insights into their constituent monopoles and offering explicit parametrizations for certain symmetric cases.

Contribution

It introduces exact multi-caloron solutions with non-trivial holonomy and develops methods to understand their constituent monopoles, including explicit parametrizations for axially symmetric cases.

Findings

Exact solutions reveal independent monopole constituents.

Impurity scattering simplifies expressions for solutions.

Explicit parametrizations achieved without solving quadratic constraints.

Abstract

We discuss the construction of multi-caloron solutions with non-trivial holonomy, both as approximate superpositions and exact self-dual solutions. The charge k SU(n) moduli space can be described by kn constituent monopoles. Exact solutions help us to understand how these constituents can be seen as independent objects, which seems not possible with the approximate superposition. An "impurity scattering" calculation provides relatively simple expressions. Like at zero temperature an explicit parametrization requires solving a quadratic ADHM constraint, achieved here for a class of axially symmetric solutions. We will discuss the properties of these exact solutions in detail, but also demonstrate that interesting results can be obtained without explicitly solving for the constraint.