Multi-Calorons Revisited

TL;DR

This paper analytically revisits SU(2) charge 2 calorons using Nahm data, classifying solutions, exploring moduli space dimensions, and examining monopole and instanton limits to deepen understanding of these periodic instantons.

Contribution

It provides an analytical solution to Nahm equations for SU(2) charge 2 calorons and classifies matching conditions, expanding the understanding of their moduli space and limits.

Findings

Analytic solutions for Nahm data in terms of Jacobi elliptic functions.

Classification of matching conditions for charge 2 calorons.

Identification of a 16-dimensional maximal moduli space for charge 2.

Abstract

Analytic Nahm data is re-examined for SU(2) calorons, or periodic instantons, of instanton charge 2. The Nahm equations are solved analytically in terms of Jacobi elliptic functions and the possible matching conditions are classified. The dimensions of framed moduli space for charge 2 caloron is enumerated and the maximal parameter, which is 16 for charge 2, case is identified. The monopole and instanton limits are also considered. It is found that the Nahm data which does not correspond to the standard monopoles plays significant role for calorons.