RG flows, cycles, and c-theorem folklore

Abstract

Monotonic renormalization group flows of the "c" and "a" functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples, that this is not necessarily true. Simultaneous monotonic and cyclic flows can be compatible if the flow-function is multi-valued in the couplings.Comment: 3 pages, 5 figure