Scale without Conformal Invariance at Three Loops

Abstract

We carry out a three-loop computation that establishes the existence of scale without conformal invariance in dimensional regularization with the MS scheme in d=4-epsilon spacetime dimensions. We also comment on the effects of scheme changes in theories with many couplings, as well as in theories that live on non-conformal scale-invariant renormalization group trajectories. Stability properties of such trajectories are analyzed, revealing both attractive and repulsive directions in a specific example. We explain how our results are in accord with those of Jack & Osborn on a c-theorem in d=4 (and d=4-epsilon) dimensions. Finally, we point out that limit cycles with turning points are unlike limit cycles with continuous scale invariance.

21 pages, 3 figures, Erratum added

References in corpus (5)

• On Renormalization Group Flows in Four Dimensions
• The Constraints of Conformal Symmetry on RG Flows
• Limit Cycles and Conformal Invariance
• RG flows, cycles, and c-theorem folklore
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• Consequences of Weyl Consistency Conditions
• Limit Cycles in Four Dimensions
• The a-function for gauge theories
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• Superembedding methods for 4d N-extended SCFTs
• On Limit Cycles in Supersymmetric Theories
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• Scale vs Conformal invariance from Entanglement Entropy
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• Non-Perturbative Constraints on Light Sparticles from Properties of the RG Flow
• Correlators in phase-ordering from Schrödinger-invariance
• Weyl Consistency Conditions from a local Wilsonian Cutoff