High-gradient operators in the psl(2|2)psl(2|2) Gross–Neveu model

It has been observed more than 25 years ago that sigma model perturbation theory suffers from strongly RG-relevant high-gradient operators. The phenomenon was first seen in 1-loop calculations for the O(N)O(N) vector model and it is known to persist at least to two loops. More recently, Ryu et al. suggested that a certain deformation of the psl(N|N)psl(N|N) WZNW-model at level k=1k=1, or equivalently the psl(N|N)psl(N|N)  Gross–Neveu model, could be free of RG-relevant high-gradient operators and they tested their suggestion to leading order in perturbation theory. In this note we establish the absence of strongly RG-relevant high-gradient operators in the psl(2|2)psl(2|2) Gross–Neveu model to all loops. In addition, we determine the spectrum for a large subsector of the model at infinite coupling and observe that all scaling weights become half-integer. Evidence for a conjectured relation with the CP1|2CP1|2 sigma model is not found.