Induced gravitational topological term and the Einstein-Cartan modified theory
J. R. Nascimento, A. Yu. Petrov, P. J. Porfírio
Abstract
It is well known that only the axial piece of the torsion couples minimally to fermions in a Riemann-Cartan geometry, while the other ones decouple. In this paper, we consider the Dirac field minimally coupled to a dynamical background with torsion and compute its contribution to the fermionic one-loop effective action. Such a contribution owns the topological nature since it can be linked with topological invariants from Riemann-Cartan spaces, like Nieh-Yan and Pontryagin (Chern-Pontryagin) terms. Furthermore, we propose a novel modified theory of gravity constructed by adding the aforementioned one-loop contribution to the Einstein-Cartan action. The modified field equations reduce to those ones of GR under certain circumstances, providing therefore trivial solutions. However, in particular, we find a nontrivial solution where the modified field equations do not reduce to the GR ones.