RG flows, cycles, and c-theorem folklore

TL;DR

This paper challenges the common belief that monotonic RG flows prevent cyclic or chaotic behaviors, showing that multi-valued flow functions can allow both monotonicity and cycles simultaneously.

Contribution

It introduces the idea that multi-valued flow functions can reconcile monotonic RG flows with cyclic or chaotic trajectories, countering traditional folklore.

Findings

Multi-valued flow functions can coexist with monotonic RG flows.

Cyclic or chaotic RG trajectories are possible with multi-valued flow functions.

Simple examples demonstrate compatibility of monotonicity and cycles.

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.