Limitations on the topologicalBFscheme in Riemann-Cartan spacetime with torsion

Abstract

Cartan's structure equations in the Riemann-Cartan framework and some topological invariants of gravity are reanalyzed from the perspective of BF theories. This is related to a variational approach to Chern-Simons terms and Bianchi identities employing Lagrange multipliers. Here, it is pointed out that the BF scheme has some limitations to the effect that a coupling to matter would leave the minimal coupling prescription of gauge theories. In the case of gravity, the field equations would, generically, become higher order with a coupling to the relocalized Belinfante-Rosenfeld energy-momentum current.