Induced non-Abelian Chern–Simons effective action in very special relativity

Abstract

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 $$(2+1)$$ -dimensional spacetime. We show that there are new graphs contributing to the amplitudes of gluon n-point functions, e.g. $$\langle GG\rangle $$ , $$\langle GGG \rangle $$ and $$\langle GGGG \rangle $$ , 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 $$\langle GG\rangle $$ 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 $$\langle GG\rangle $$ , $$\langle GGG \rangle $$ and $$\langle GGGG \rangle $$ . 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.