A simple remark on three dimensional gauge theories

Abstract

Classical three dimensional Yang-Mills is seen to be related to the topological Chern-Simons term through a nonlinear but fully local and covariant gauge field redefinition. A classical recursive cohomological argument is provided.Comment: 8 pages, LateX2e fil

Field redefinitions and massive BF models in arbitrary space–time dimensions

“…This result, valid for any dimension, represents a generalization of the results obtained in [8,9] for topological three dimensional massive YangMills theory. Let us underline that this property seems to be valid for all topological massive theories in any dimension.…”

“…As shown by the authors [9], the coefficients ϑ n µ (D, F ) are local and covariant and depend only on the field strength F µν and the covariant derivative…”

“…(2.3). This justification is based on [8,9] and is quite formal. Let B and A be the anti-fields of B and A.…”

“…In order to justify this, we follow the same arguments used for the Chern-Simons case [9]. The full BRST differential s, in this case, has non-linear dependence on the fields and anti-fields.…”

“…An important result was obtained a few years ago by Giavarini and collaborators about the finiteness of topological massive Yang-Mills theory in three dimensions, with a careful analysis of higher loops of the Feynman integrals [7]. More recently, Lemes et al [8,9], showed that the topological three dimensional massive Yang-Mills theory can be cast in the form of a pure Chern-Simons action through a non-linear but local field redefinition,…”