Consistent Deformations for a Non-Standard D = 6 Topological BF Model from a BRST-Symmetry-Based Cohomological Approach

Abstract

This paper falls under the heading of constructing consistent self-couplings in topological BF models. Our endeavor is of interest in the context of pure gravity, General Relativity, and super-gravity in Ashtekar formalism, which allow for certain economic formulations in terms of self-coupled BF theories in the presence of certain extra-constraints. More precisely, herein we address the construction of a special class of D=6 self-interactions for a collection of topological BF models with a non-standard field spectrum. Our methodology relies on a deformation method based on the relationship between antifield–BRST symmetry and the non-trivial gauge symmetries of a given field theory and implemented via the computation of certain precise spaces of the local BRST cohomology corresponding to the free limit. This cohomological BRST approach is applied to the starting free model under standard “selection rules” from Quantum Field Theory. Our findings are completely new and reveal a self-interacting topological BF model in D=6 with a complex gauge structure that is entirely read from the expression of the fully deformed solution to the classical master equation (the canonical generator of the antifield–BRST symmetry), and includes a generalization of the famous D=2 gravity in BF formulation.