Chiral-charge conservation and gauge fields

Abstract

An example of a gauge field theory with classical dyon solutions which violates anomalous chiral-charge conservation is presented. We also show that the pseudoparticle solution to the four-dimensional pure Yang-Mills equations is equivalent to a kink solution in one dimension. The net change in chirality, the Pontryagin index, and kink number are equivalent. This suggests an intimate connection between the spherically symmetric four-dimensional Euclidean gauge field theory and one-dimensional scalar field theories.