2021/08/31 by J. R. Nascimento, A. Yu. Petrov, P. J. Porfírio · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Effective action #Gravitation #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Optimal control #Physics #Pontryagin's minimum principle #Pure mathematics #Riemann hypothesis #Topology (electrical circuits) #Torsion (gastropod) #gr-qc
paper · pdf · doi:10.1103/physrevd.105.044053
published as Phys. Rev. D 105, 044053 (2022) · 15 pages, no figures, matches published version
openalex created_date 2021/08/16 · arxiv created 2022/02/25 · openalex publication_date 2022/02/25 · arxiv updated 2022/02/28 · openalex updated_date 2026/08/05
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.