Cyclic calorons

The Nahm data of periodic instantons, often called calorons, with spatial CN-symmetries are considered, by applying Sutcliffeʼs ansatz for the monopoles with CN-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 C3-symmetric caloron is obtained.