Superspace approach to anomalous dimensions in {\cal N}=4 SYM

TL;DR

This paper introduces a superspace method using dimensional regularization to compute anomalous dimensions of composite operators in { m N}=4 SYM, simplifying calculations and confirming known results.

Contribution

It provides a straightforward prescription for calculating anomalous dimensions in { m N}=4 SYM using superspace and dimensional regularization, including a check on the Konishi superfield.

Findings

Anomalous dimensions cause higher order poles in two-point functions.

The lowest contribution is obtained from the 1/ε^2 pole coefficient.

The anomalous dimension of a specific double trace superfield vanishes for all N.

Abstract

In a {\cal N}=1 superspace setup and using dimensional regularization, we give a general and simple prescription to compute anomalous dimensions of composite operators in {\cal N}=4, SU(N) supersymmetric Yang-Mills theory, perturbatively in the coupling constant g. We show in general that anomalous dimensions are responsible for the appearance of higher order poles in the perturbative expansion of the two-point function and that their lowest contribution can be read directly from the coefficient of the 1/\epsilon^2 pole. As a check of our procedure we rederive the anomalous dimension of the Konishi superfield at order g^2. We then apply this procedure to the case of the double trace, dimension 4, superfield in the 20 of SU(4) recently considered in the literature. We find that its anomalous dimension vanishes for all N in agreement with previous results.