Periodic Instantons with non-trivial Holonomy

TL;DR

This paper derives explicit solutions for charge one calorons with non-trivial holonomy in SU(2), using Nahm and ADHM methods, and explores their properties and implications for QCD.

Contribution

It provides a detailed derivation of SU(2) calorons with non-trivial holonomy, including explicit Green's functions and analysis of the moduli space.

Findings

Explicit Green's function for calorons derived

Moduli space characterized as R^3 x S^1 x Taub-NUT/Z_2

Holonomy related to Taub-NUT mass parameter

Abstract

We present the detailed derivation of the charge one periodic instantons - or calorons - with non-trivial holonomy for SU(2). We use a suitable combination of the Nahm transformation and ADHM techniques. Our results rely on our ability to compute explicitly the relevant Green's function in terms of which the solution can be conveniently expressed. We also discuss the properties of the moduli space, R^3 X S^1 X Taub-NUT/Z_2 and its metric, relating the holonomy to the Taub-NUT mass parameter. We comment on the monopole constituent description of these calorons, how to retrieve topological charge in the context of abelian projection and possible applications to QCD.