Renormalization Group Functional Equations

Abstract

Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods produce continuous flows from step-scaling σ functions, and lead to exact functional relations for the local flow β functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of σ are sometimes not true fixed points under continuous changes in scale, and zeroes of β do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.

A physical model with a limit cycle added as section IV, along with references

References in corpus (16)

• Seeing a c-theorem with holography
• Lattice Study of Conformal Behavior in SU(3) Yang-Mills Theories
• Supersymmetry Inspired QCD Beta Function
• Can the QCD running coupling have a causal analyticity structure?
• Finite-Size Scaling at $\xi /L\gg 1$
• Limit cycles in quantum theories
• Asymptotic Pade Approximant Predictions: up to Five Loops in QCD and SQCD
• Russian Doll Renormalization Group and Superconductivity
• The Ubiquitous 'c': from the Stefan-Boltzmann Law to Quantum Information
• Russian Doll Renormalization Group, Kosterlitz-Thouless Flows, and the Cyclic sine-Gordon model
• Universality, marginal operators, and limit cycles
• Log-periodic behavior of finite size effects in field theories with RG limit cycles
• Renormalization group limit-cycles and field theories for elliptic S-matrices
• Evolution profiles and functional equations
• Logistic Map Potentials
• Chaotic Maps, Hamiltonian Flows, and Holographic Methods

Cited by in corpus (9)

• RG flows, cycles, and c-theorem folklore
• Solving RG equations with the Lambert W function
• Lines of Fisher's zeros as separatrices for complex renormalization group flows
• Branched Hamiltonians and Supersymmetry
• New applications of the renormalization group method in physics -- a brief introduction
• Koopman Operator Dynamical Models: Learning, Analysis and Control
• Approximate Solutions of Functional Equations
• Potentials Unbounded Below
• Renormalisation group flow of the Jaynes-Cummings model