Inconsistency of Naive Dimensional Regularizations and Quantum Correction to Non-Abelian Chern-Simons-Matter Theory Revisited

We find the inconsistency of dimensional reduction and naive dimensional regularization in their applications to Chern-Simons type gauge theories. Further we adopt a consistent dimensional regularization to investigate the quantum correction to non-Abelian Chern-Simons term coupled with fermionic matter. Contrary to previous results, we find that not only the Chern-Simons coefficient receives quantum correction from spinor fields, but the spinor field also gets a finite quantum correction.