Anomalous dimensions in N=4 SYM theory at order g^4

TL;DR

The paper computes four-point functions of lowest-dimension scalar composites in the ${\cal N}=4$ supercurrent multiplet at order $g^{4}$ using ${\cal N}=1$ superspace. The authors show that short-distance logarithms correspond to anomalous dimensions of unprotected operators exchanged in the OPE, and they extract the two-loop anomalous dimension of the Konishi multiplet, finding $\gamma_1 = {3N \over 16\pi^2}$ and $\gamma_{2} = -{3 g^{4} N^2 \over 16 (4\pi^2)^2}$. They also confirm non-renormalisation in certain representations and discuss how their ${\cal N}=1$ approach aligns with ${\cal N}=2$ harmonic superspace results, with implications for finite ${\cal N}=1$ theories and AdS/CFT. Overall, the work demonstrates the calculability of nontrivial correlators in ${\cal N}=4$ SYM at high perturbative order and provides precise data on operator mixing and anomalous dimensions relevant to holographic duals.

Abstract

We compute four-point correlation functions of scalar composite operators in the N=4 supercurrent multiplet at order g^4 using the N=1 superfield formalism. We confirm the interpretation of short-distance logarithmic behaviours in terms of anomalous dimensions of unprotected operators exchanged in the intermediate channels and we determine the two-loop contribution to the anomalous dimension of the N=4 Konishi supermultiplet.

Figures (3)

• Figure 1: Diagrams with only chiral lines.
• Figure 2: Diagrams with two vector lines.
• Figure 3: Diagrams with one vector line.