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.

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

References in corpus (19)

• On Renormalization Group Flows in Four Dimensions
• Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry
• FORM version 4.0
• The Constraints of Conformal Symmetry on RG Flows
• The $a$-theorem and the Asymptotics of 4D Quantum Field Theory
• Beta functions and anomalous dimensions up to three loops
• What Maxwell Theory in D<>4 teaches us about scale and conformal invariance
• Limit Cycles and Conformal Invariance
• Evidence for the Strongest Version of the 4d a-Theorem, via a-Maximization Along RG Flows
• On renormalization group flows and the a-theorem in 6d
• Three loop gauge beta-function for the most general single gauge-coupling theory
• Scale without Conformal Invariance: An Example
• Scale without Conformal Invariance: Theoretical Foundations
• Scale without Conformal Invariance at Three Loops
• On R-symmetric Fixed Points and Superconformality
• Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly
• Gravity Dual for Cyclic Renormalization Group Flow without Conformal Invariance
• Cyclic unparticle physics
• Is There Scale Invariance in N=1 Supersymmetric Field Theories ?

Cited by in corpus (26)

• Convexity and Liberation at Large Spin
• The $a$-theorem and the Asymptotics of 4D Quantum Field Theory
• Limit Cycles and Conformal Invariance
• Effective Theory of a Light Dilaton
• On Scale and Conformal Invariance in Four Dimensions
• The a theorem for Gauge-Yukawa theories beyond Banks-Zaks
• Running couplings with a vanishing scale anomaly
• Consequences of Weyl Consistency Conditions
• Supercurrent, Supervirial and Superimprovement
• Perturbative c-theorem in d-dimensions
• RG Limit Cycles and Unconventional Fixed Points in Perturbative QFT
• Dualities from higher-spin supergravity
• The a-theorem and conformal symmetry breaking in holographic RG flows
• Weyl Consistency Conditions in Non-Relativistic Quantum Field Theory
• On Ambiguities and Divergences in Perturbative Renormalization Group Functions
• Superembedding methods for 4d N-extended SCFTs
• Is boundary conformal in CFT?
• On Limit Cycles in Supersymmetric Theories
• Scale Invariance vs. Conformal Invariance: Holographic Two-Point Functions in Horndeski Gravity
• Scale vs Conformal invariance from Entanglement Entropy
• (Delta a) curiosities in some 4d susy RG flows
• Gravity duals of cyclic RG flows, with strings attached
• Weyl Consistency Conditions from a local Wilsonian Cutoff
• Emergent Supersymmetry in the Marginal Deformations of N=4 SYM
• General Gauge-Yukawa-Quartic $\beta$-Functions at 4-3-2--Loop Order
• Gradient flows for $\beta$ functions via multi-scale renormalization group equations