ABSTRACT

This chapter explores the reasons for the analogies. Roughly speaking, it appears that small pieces of the flux lines in the gauge case move as if they were point-like excitations of a chiral field. The gauge field itself can be considered as a chiral field defined on the space of all possible loops. But they provide research workers with a bridge between gauge theories, chiral fields and the theory of strings. They may also help in a search for hidden symmetries in many-dimensional systems. One cannot help feeling that many beautiful secrets are concealed in loop space. Before coming to it let research workers sum up what their know about the connections between gauge fields and chiral fields. The chapter shows that gauge fields are chiral fields defined on the loop space. Unfortunately, up to now it has not been possible to extract any practical, dynamical information from this fact.