Cyclic Calorons

Abstract

The Nahm data of periodic instantons, often called calorons, with spatial $C_N$-symmetries are considered, by applying Sutcliffe's ansatz for the monopoles with $C_N$-symmetries. The bulk data of calorons are shown to enjoy the periodic Toda lattice, and the solutions are given in terms of elliptic theta functions. The case of N=3 calorons are investigated in detail. It is found that the "scale parameters" of these calorons have upper bounds in their values, so that they do not have the large scale, or monopole, limits. The instanton limit of the $C_3$-symmetric caloron is obtained.

21 pages, 2 figures

References in corpus (6)

• Stationary ring solitons in field theory - knots and vortons
• Irrational vs. rational charge and statistics in two-dimensional quantum systems
• Large scale and large period limits of symmetric calorons
• Multi-Calorons Revisited
• Cyclic Monopoles, Affine Toda and Spectral Curves
• Determinant of the SU(N) caloron with nontrivial holonomy

Cited by in corpus (3)

• Symmetric calorons and the rotation map
• Aspects of $C_3$-symmetric calorons from numerical Nahm transform
• Symmetric calorons of higher charges and their large period limits