Exact T-duality between Calorons and Taub-NUT spaces

TL;DR

This paper establishes an exact duality between caloron solutions with specific topological charge and Polyakov loop parameters and Taub-NUT spaces, revealing a deep geometric connection relevant to finite temperature field theory and string theory.

Contribution

It explicitly computes all SU(2) caloron solutions with topological charge one and links their moduli space to Taub-NUT geometry using Nahm and ADHM methods.

Findings

Moduli space is a product of R^3 x S^1 and Taub-NUT space.

Mass of the Taub-NUT space depends on the Polyakov loop parameter.

Explicit solutions demonstrate the T-duality between calorons and Taub-NUT spaces.

Abstract

We determine all SU(2) caloron solutions with topological charge one and arbitrary Polyakov loop at spatial infinity (with trace 2.cos(2.pi.omega)), using the Nahm duality transformation and ADHM. By explicit computations we show that the moduli space is given by a product of the base manifold R^3 X S^1 and a Taub-NUT space with mass M=1/sqrt{8.omega(1-2.omega)}, for omega in [0, 1/2], in units where S^1=R/Z. Implications for finite temperature field theory and string duality between Kaluza-Klein and H-monopoles are briefly discussed