Anomalous dimensions at small spins

Abstract

In perturbation theory, the anomalous dimensions of twist-two operators have poles at negative or small positive integer values of spin and therefore must be resummed at these points. It was observed earlier that a certain quadratic combination of the anomalous dimensions remains finite at the right-most singularities, providing an efficient tool for resummation. In this paper, we analyze the small-spin behavior of the anomalous dimensions for all types of twist-two operators in the $O(N)$-symmetric $\varphi^4$ model at the four-loop level, in the complex $\varphi^3$ model at the three-loop level, and the Gross-Neveu-Yukawa model at the two-loop level. We find that the behavior of the anomalous dimensions at singular points is consistent with theoretical expectations, and we present expressions for the resummed anomalous dimensions.