High-Gradient Operators in the psl(2|2) Gross-Neveu Model

TL;DR

This paper proves that the psl(2|2) Gross-Neveu model lacks RG-relevant high-gradient operators at all loops and explores its spectrum at infinite coupling, providing insights into its structure and relation to other models.

Contribution

It establishes the absence of RG-relevant high-gradient operators in the psl(2|2) Gross-Neveu model at all orders and analyzes its spectrum at infinite coupling.

Findings

No RG-relevant high-gradient operators at all loops.

Spectrum at infinite coupling has half-integer scaling weights.

No evidence found for relation to the CP^1|2 sigma model.

Abstract

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) 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) WZNW-model at level k = 1, or equivalently the 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) 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 CP^1|2 sigma model is not found.