Perturbative Study of the Leigh-Strassler Deformations of N=4 Supersymmetric Yang-Mills Theory
Leigh-Strassler theories are marginal deformations of N=4 SYM and hence are superconformal field theories studied in the context of AdS/CFT. By computing anomalous dimensions for scalar composite operators upto dimension 6 at one-loop planar level, we obtain chiral primary states of LS theory. These states appear in representations of discrete group trihedral \Delta(27). This symmetry group is also seen to be preserved quantum mechanically. Computing three-loop anomalous dimension of the chiral superfield, we further observe that there are coupling constant redefinitions that preserve conformal invariance. We also point out that the same redefinitions may remove the correction to superpotential at two-loop.