A 2D gravity ‘facet’ of a BF theory in the presence of some massless real scalar fields

Abstract Beginning with a 2 D linear model with the Lagrangian action consisting of the sum between that of a topological field theory of BF-type and that of a system of massless real scalar fields, one determines the general interaction vertex that can be added to the initial theory, while preserving the field spectrum and the range of independent degrees of freedom. The analysis is performed using the deformation technique within the framework of antifield-BRST symmetry, aided by specific techniques of local (co-)homology. In the considered space-time dimension, it is shown that the scalar fields from the BF field spectrum ’generate’ some ’gravitational potential facet’ in the context of the interaction with the considered matter fields.