Finite BRST-antiBRST Transformations for the Theories with Gauge Group

Following our recent study [P.Yu. Moshin, A.A. Reshetnyak, Nucl. Phys. B 888 (2014) 92], we discuss the notion of finite BRST-antiBRST transformations, with a doublet $\lambda_{a}$, $a=1,2$, of anticommuting (both global and field-dependent) Grassmann parameters. It turns out that the global finite BRST-antiBRST transformations form a 2-parametric Abelian supergroup. We find an explicit Jacobian corresponding to this change of variables in the theories with a gauge group. Special field-dependent BRST-antiBRST transformations for the Yang--Mills path integral with $s_{a}$-potential (functionally-dependent) parameters $\lambda_{a}=s_{a}\Lambda$ generated by a finite even-valued functional $\Lambda$ and the anticommuting generators $s_{a}$ of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations and leads to the presence of modified Ward identities. The form of transformation parameters that induces a change of the gauge in the path integral is found and is exactly evaluated for connecting two arbitrary $R_{\xi}$-like gauges. The finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional $h_{ 0 }$, in the Landau gauge of the BRST-antiBRST setting in the Gribov--Zwanziger model, and to find $h_{\xi}$ corresponding to general $R_{\xi}$-like gauges in the form compatible with a gauge-independent $S$-matrix.