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• W2080781118 abstract "There 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." @default.
• W2080781118 created "2016-06-24" @default.
• W2080781118 creator A5022922171 @default.
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• W2080781118 date "2013-01-01" @default.
• W2080781118 modified "2023-10-15" @default.
• W2080781118 title "Limit cycles and conformal invariance" @default.
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• W2080781118 doi "https://doi.org/10.1007/jhep01(2013)184" @default.
• W2080781118 hasPublicationYear "2013" @default.
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