Conformal constraints for anomalous dimensions of leading twist operators

TL;DR

This paper investigates using conformal constraints to compute anomalous dimensions of leading-twist operators, demonstrating feasibility in a toy model but with limited practical simplification over standard methods.

Contribution

It explores the potential of conformal constraints to simplify calculations of anomalous dimensions, providing a nontrivial check in a toy model of $$ theory.

Findings

Approach is valid but offers limited technical simplification.

Provides a nontrivial consistency check of the method.

Demonstrates feasibility in a toy model setting.

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 $\varphi^3$ 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.