Supergraphs and the cubic Leigh-Strassler model

TL;DR

This paper explores supergraphs in N=4 Super Yang-Mills and Leigh-Strassler theories, proposing all-loop conjectures for certain operators' anomalous dimensions and identifying classes with zero anomalous dimensions in the planar limit.

Contribution

It introduces an all-loop conjecture for rational supergraph contributions and analyzes anomalous dimensions of specific operators in Leigh-Strassler theories.

Findings

Identified operators with zero anomalous dimensions to all loop orders.

Derived a simple expression for the rational part of anomalous dimensions up to five loops.

Computed anomalous dimensions for certain operators up to four loops.

Abstract

We discuss supergraphs and their relation to "chiral functions" in N=4 Super Yang-Mills. Based on the magnon dispersion relation and an explicit three-loop result of Sieg's we make an all loop conjecture for the rational contributions of certain classes of supergraphs. We then apply superspace techniques to the "cubic" branch of Leigh-Strassler N=1 superconformal theories. We show that there are order 2^L/L single trace operators of length L which have zero anomalous dimensions to all loop order in the planar limit. We then compute the anomalous dimensions for another class of single trace operators we call one-pair states. Using the conjecture we can find a simple expression for the rational part of the anomalous dimension which we argue is valid at least up to and including five-loop order. Based on an explicit computation we can compute the anomalous dimension for these operators to four loops.