Multi-calorons and their moduli

TL;DR

This paper studies calorons in Yang-Mills theory on S^1 x R^3 with non-centre holonomy, revealing they decompose into magnetic monopoles with fractional topological charge, and explores their solutions, zero-modes, and geometric structure.

Contribution

It introduces a new interpretation of calorons as collections of magnetic monopoles and provides exact solutions, zero-modes, and geometric analysis of their moduli space.

Findings

Calorons decompose into nk magnetic monopoles with fractional charge.

Exact solutions and fermionic zero-modes for calorons are constructed.

Analysis of the hyperkähler and twistor geometry of the caloron moduli space.

Abstract

Pure Yang-Mills instantons are considered on S^1 x R^3 -- so-called calorons. The holonomy -- or Polyakov loop around the thermal S^1 at spatial infinity -- is assumed to be a non-centre element of the gauge group SU(n) as most appropriate for QCD applications in the confined phase. It is shown that a charge k caloron can be seen as a collection of nk massive magnetic monopoles each carrying fractional topological charge. This interpretation offers a physically appealing way of introducing monopole degrees of freedom into pure gluodynamics: as constituents of finite temperature instantons. New and exact solutions are found along with the fermionic zero-modes of the Dirac operator. The properties of the zero-modes are analysed as well as the hyperkahler and twistor geometry of the caloron moduli space. Lattice gauge theoretic applications are also mentioned.