Renormalization group study of the Chern-Simons field coupled to scalar matter in a modified BPHZ subtraction scheme

Abstract

We apply a soft version of the Bogolubov-Parasiuk-Hepp-Zimmermann subtraction scheme to the computation of two-loop corrections from an Abelian Chern-Simons field coupled to (massive) scalar matter with a $\ensuremath{\lambda}({\ensuremath{\Phi}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\Phi}{)}^{2}$ and $\ensuremath{\nu}({\ensuremath{\Phi}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\Phi}{)}^{3}$ self-interactions. The two-loop renormalization group functions are calculated. We compare our results with those in the literature.