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

TL;DR

This paper investigates how very special relativity (VSR) modifies the one-loop induced non-Abelian gauge field actions, revealing new contributions and altered equations of motion in a (2+1)-dimensional setting.

Contribution

It introduces the first analysis of VSR effects on non-Abelian Chern-Simons and Yang-Mills actions, including new graphs and modifications to gauge field equations.

Findings

VSR generates new graphs contributing to gluon n-point functions.

VSR corrections alter the induced kinetic and Chern-Simons terms.

Pure gauge solutions are invalidated by VSR effects.

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.