Limit cycles and conformal invariance

By J. Fortin, B. Grinstein, A. Stergiou. 2012

138 citations recorded by the source corpus.

A bstractThere is a widely held belief that conformal field theories (CFTs) require zero beta functions. Nevertheless, the work of Jack and Osborn implies that the beta functions are not actually the quantites that decide conformality, but until recently no such behavior had been exhibited. Our recent work has led to the discovery of CFTs with nonzero beta functions, more precisely CFTs that live on recurrent trajectories, e.g., limit cycles, of the beta-function vector field. To demonstrate this we study the S function of Jack and Osborn. We use Weyl consistency conditions to show that it vanishes at fixed points and agrees with the generator Q of limit cycles on them. Moreover, we compute S to third order in perturbation theory, and explicitly verify that it agrees with our previous determinations of Q. A byproduct of our analysis is that, in perturbation theory, unitarity and scale invariance imply conformal invariance in four-dimensional quantum field theories. Finally, we study some properties of these new, “cyclic” CFTs, and point out that the a-theorem still governs the asymptotic behavior of renormalization-group flows.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6f205c5eea5df3f166e97f662aaad7571c4018b3

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Citations in the corpus

Deformations of superconformal theories (2016, background): “See [3] for a review of what is known in other spacetime dimensions, and [4–9] for developments in d = 4.”
Conformal invariance in the long-range Ising model (2015, background): “” 30 See [48] for a review and in particular [49–51] for recent nontrivial progress in 4d.”