https://doi.org/10.1140/epjp/s13360-022-02941-y
Regular Article
Induced non-Abelian Chern–Simons effective action in very special relativity
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
3
School of Mathematics, Statistics and Physics, Newcastle University, NE1 7RU, Newcastle upon Tyne, UK
Received:
7
February
2022
Accepted:
9
June
2022
Published online:
26
June
2022
In this paper, we study the one-loop induced effective action for a non-Abelian gauge field in the very special relativity (VSR) framework in a -dimensional spacetime. We show that there are new graphs contributing to the amplitudes of gluon n-point functions, e.g.
,
and
, originating from the non-local couplings generated in VSR. Using the one-loop analysis of the relevant graphs, we evaluate the VSR corrections to the induced kinetic term of the non-abelian gauge field action in three dimensions. Next, by applying the Ward identity, we determine the general tensorial structure for the amplitude of
in VSR, which is valid at any order of the loop analysis. Moreover, we discuss the leading VSR corrections to the non-abelian Chern–Simons and Yang–Mills action through the analysis of
,
and
. In order to highlight the VSR effects, we present the VSR modification of non-Abelian Chern–Simons effective action and then obtain the equation of motion for the non-Abelian gauge field. As a result, we observe that the well-known pure gauge solution does not hold in the presence of VSR effects.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022