one-loop. In the 1994 article Nonrenormalization Theorem for Gauge Coupling in 2+1D the authors find the renormalization of the level can only be a finite shift, independent of the energy scale, and extended this result to topologically massive theories in which one includes a kinetic term for the gluons. In Notes on Superconformal Chern-Simons-Matter Theories the authors then showed that this shift needs to occur at one loop, because any renormalization at higher loops would introduce inverse powers of the level, which are nonintegral and so would be in conflict with the quantization condition. References N. Seiberg (1993) "Naturalness Versus Supersymmetric Non-renormalization Theorems" External links Non-Renormalization Theorems in Supersymmetry Supersymmetric quantum field theory Renormalization group