Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 8, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP08(2012)085
Keywords
Space-Time Symmetries; Renormalization Group; Conformal and W Symmetry
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Funding
- US Department of Energy [DOE-FG03-97ER40546]
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We carry out a three-loop computation that establishes the existence of scale without conformal invariance in dimensional regularization with the MS scheme in unitary theories 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.
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