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

By computing anomalous dimensions of gauge invariant composite operators (ψ̄ψ) and (φφ) in Chern-Simons fermion and boson models, we address that Chern-Simons interactions make these operators more relevant or less irrelevant in the low energy region. We obtain a critical Chern-Simons fermion coupling, 1 κ2c = 6 19 , for a phase transition at which the leading irrelevant four-fermion operator (ψ̄ψ)2 becomes marginal, and a critical Chern-Simons boson coupling, 1 κ2c = 6 34 , for a similar phase transition for the leading irrelevant operator (φ ∗φ)4. We see this phenomenon also in the 1/N expansion. 0∗ [email protected] 0† Present address: Department of Physics, Brown University, Providence, RI 02912 USA. [email protected]