Conformal constraints for anomalous dimensions of leading twist operators

Abstract

Leading-twist operators have a remarkable property that their divergence vanishes in a free theory. Recently it was suggested that this property can be used for an alternative technique to calculate anomalous dimensions of leading-twist operators and allows one to gain one order in perturbation theory so that, i.e., two-loop anomalous dimensions can be calculated from one-loop Feynman diagrams, etc. In this work we study feasibility of this program on a toy-model example of the ${\phi }^3$ theory in six dimensions. Our conclusion is that this approach is valid, although it does not seem to present considerable technical simplifications as compared to the standard technique. It does provide one, however, with a very nontrivial check of the calculation as the structure of the contributions is very different.

14 pages, 6 figures

References in corpus (4)

• Anomalous dimensions of high-spin operators beyond the leading order
• The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
• Evolution equations beyond one loop from conformal symmetry
• Anomalous dimensions of leading twist conformal operators

Cited by in corpus (6)

• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Anomalous dimensions in CFT with weakly broken higher spin symmetry
• Notes on Spinning Operators in Fermionic CFT
• Classical equation of motion and Anomalous dimensions at leading order
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• On (Un)Broken Higher-Spin Symmetry in Vector Models