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. $⟨GG⟩$, $⟨GGG⟩$ and $⟨GGGG⟩$, 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 $⟨GG⟩$ 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 $⟨GG⟩$, $⟨GGG⟩$ and $⟨GGGG⟩$. 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.

arXiv comment21 pages, published version

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