C-theorem: Difference between revisions

Revision as of 19:08, 21 July 2012

Revision as of 22:12, 8 October 2012

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Until recently, it had not been possible to prove an analog ''C''-theorem in higher-dimensional quantum field theory. However, in 2011, Zohar Komargodski and Adam Schwimmer proposed a proof for the physically more important four-dimensional case, which has gained acceptance.<ref>{{cite doi| 10.1038/nature.2011.9352|noedit}}</ref><ref name="komargodski">{{cite doi|10.1007/JHEP12(2011)099|noedit}}</ref> (Still, simultaneous monotonic and cyclic ([[limit cycle]]) or even chaotic RG flows are compatible with such flow functions when multivalued in the couplings, as evinced in specific systems.<ref>{{cite doi|10.1103/PhysRevLett.108.131601|noedit}}</ref>)

In 2011 and 2012, Fortin, Grinstein and Stergiou discovered limit cycles and ergodic behavior in RG flows of unitary quantum field theories in <math>4-\epsilon</math><ref>{{cite doi|10.1016/j.physletb.2011.08.060|noedit}}</ref> and four spacetime dimensions. These examples describe RG flows accessible in perturbation theory and thus do not have multi-valued ''C''-functions. Any possible ''C''-function is constant both in scale-invariant trajectories and at fixed points of the RG. These recurrent behaviors in the RG are associated with theories that are scale-invariant without being conformally invariant.

==See also==