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.

3 pages, 5 figures

References in corpus (3)

• On Renormalization Group Flows in Four Dimensions
• The Ubiquitous 'c': from the Stefan-Boltzmann Law to Quantum Information
• Renormalization Group Functional Equations

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• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows
• Towards a $C$-function in 4D quantum gravity
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• RG Limit Cycles and Unconventional Fixed Points in Perturbative QFT
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• Space of non-Fermi liquids
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