Field-dependent BRST–antiBRST transformations in Yang–Mills and Gribov–Zwanziger theories

Abstract

We introduce the notion of finite BRST–antiBRST transformations, both global and field-dependent, with a doublet λa, a=1,2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang–Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang–Mills vacuum functional, special field-dependent BRST–antiBRST transformations, with sa-potential parameters λa=saΛ induced by a finite even-valued functional Λ and by the anticommuting generators sa 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. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary Rξ-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST–antiBRST transformations are used to generalize the Gribov horizon functional h, given in the Landau gauge, and being an additive extension of the Yang–Mills action by the Gribov horizon functional in the Gribov–Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST–antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations.