Limit Cycles in Four Dimensions

Abstract

We present an example of a limit cycle, i.e., a recurrent flow-line of the beta-function vector field, in a unitary four-dimensional gauge theory. We thus prove that beta functions of four-dimensional gauge theories do not produce gradient flows. The limit cycle is established in perturbation theory with a three-loop calculation which we describe in detail.

Comments: 12 pages, 1 figure. Significant revision of the interpretation of our result. Improved description of three-loop calculation