Implications of the topological Chern-Simons mass in the gap equation

In this paper, we solve the gap equation of the Yang-Mills-Gribov-Zwanziger-Chern-Simons theory by considering the first order in the Chern-Simons topological mass term, $M$. As a result, we find three possible solutions to the gap equation, i.e., three different Gribov parameters, two of which can be eliminated by the regime of the theory. In addition, our conclusion about the regime of the theory is different from the literature. We also show that, in our case, there is no weak-coupling regime.

Figure 1

Plot of imaginary part of $\gamma$ when $\mathrm{\Delta }<0$, $N=3$.

Figure 2

$m_1^2$ in function of $M$ and $g$, $N=3$.

Figure 3

The left side from (3.5).