Induced Yang-Mills-Non-Abelian-Chern-Simons action in three dimensions

Abstract

In this paper, we consider the massive quarks interacting with an external non-abelian gauge field (gluon) in (1+2)-dimensional spacetime. By integrating out the quark fields, we obtain the general structure of the one-loop effective action for the gluons coupled to the quarks. Next, we compute the one-loop Feynman graphs related to one, two, three and four-point functions for the gluon, by using dimensional regularization. We explicitly show that the resulting effective action, at the low-energy limit (), leads to the non-Abelian Chern-Simons and Yang-Mills action. This induced action, arising from the quantum corrections due to the fermionic loops, also respects Lorentz and gauge invariance.