Chiral primaries in the Leigh-Strassler deformed N=4 SYM -- a perturbative study

TL;DR

This paper systematically studies chiral primaries in Leigh-Strassler deformed N=4 SYM, revealing a relationship between their U(1)_R-charge and (27) representations, and identifying conditions for vanishing anomalous dimensions.

Contribution

It provides a detailed perturbative analysis of chiral primaries up to dimension six, linking their properties to (27) symmetry representations and R-charges.

Findings

Vanishing one-loop anomalous dimension occurs only for operators in singlet or three-dimensional (27) representations.

The relationship between R-charge and (27) representation is established.

Vanishing anomalous dimensions for other operators occur only on specific coupling sub-loci.

Abstract

We look for chiral primaries in the general Leigh-Strassler deformed N=4 super Yang-Mills theory by systematically computing the planar one-loop anomalous dimension for single trace operators up to dimension six. The operators are organised into representations of the trihedral group, \Delta(27), which is a symmetry of the Lagrangian. We find an interesting relationship between the U(1)_R-charge of chiral primaries and the representation of \Delta(27) to which the operator belongs. Up to scaling dimension \Delta_0=6 (and conjecturally to all dimensions) the following holds: The planar one-loop anomalous dimension vanishes only for operators that are in the singlet or three dimensional representations of \Delta(27). For other operators, the vanishing of the one-loop anomalous dimension occurs only in a sub-locus in the space of couplings.