https://doi.org/10.1140/epjc/s10052-024-12821-7
Regular Article - Theoretical Physics
On the gauge invariance of the higher-derivative Yang–Mills–Chern–Simons action
1
Department of Physics, Shahid Beheshti University, 1983969411, Tehran, Iran
2
Departamento de Física, Universidade Federal de Lavras, Caixa Postal 3037, 37200-900, Lavras, MG, Brazil
Received:
24
March
2024
Accepted:
15
April
2024
Published online:
6
May
2024
In this work, we study the perturbative generation of the gauge invariant effective action for the non-Abelian gauge field in a 
-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.
© The Author(s) 2024
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