Driving operators relevant: A feature of the Chern-Simons interaction

By computing anomalous dimensions of gauge invariant composite operators (bar ψψ)n and (φ*φ)n in matter--Chern-Simons models, we address the fact that the Chern-Simons interactions make these operators more relevant, or less irrelevant, in the low energy region. We suggest a critical Chern-Simons fermion coupling, 1/κc2=6/19, for a phase transition at which the leading irrelevant operator (bar ψψ)2 becomes marginal, and a critical Chern-Simons boson coupling, 1/κc2=6/34, for a similar phase transition for the leading irrelevant operator (φ*φ)4. We see the phenomenon also in the 1/N expansion