1208.3674 (Jean-François Fortin et al.)

A generalized c-theorem and the consistency of scale without conformal
invariance    [PDF]

Jean-François Fortin, Benjamin Grinstein, Andreas Stergiou

We generalize the proof of the weak version of the c-theorem presented by Komargodski and Schwimmer to the case where a renormalization group flow links a fixed point to a limit cycle, or a cycle to a cycle. We show that the argument of Luty, Polchinski and Rattazzi, ruling out limit cycles in four-dimensional theories is flawed. We compute the S function of Jack and Osborn to third order in the loop expansion and show that it vanishes at fixed points and agrees with the generator Q of limit cycles on them. This vastly simplifies the search for limit cycles, as only one-loop beta functions (two-loop for Yang--Mills couplings) are required to establish their existence.

View original: http://arxiv.org/abs/1208.3674