On the gauge invariance of the higher-derivative Yang–Mills–Chern–Simons action

In this work, we study the perturbative generation of the gauge invariant effective action for the non-Abelian gauge field in a ( 2 + 1 ) -dimensional spacetime. We present a detailed analysis of the two, three and four-point functions in order to determine the non-Abelian Chern–Simons terms (parity odd) and Yang–Mills terms (parity even). Moreover, these terms are supplemented by the higher-derivative corrections which resulted in the Alekseev–Arbuzov–Baikov effective action (parity even) plus the higher-derivative (HD) corrections to the Chern–Simons terms (parity odd). In order to highlight some features about the perturbative generation of the effective action, we present a discussion based on the dimensional analysis, which allows us to establish the general structure of the permissible terms to guarantee the gauge invariance of the higher-derivative parts.