Induced gravitational topological term and the Einstein-Cartan modified theory

TL;DR

This paper explores the topological contributions of torsion in Riemann-Cartan geometry to fermionic effective actions and proposes a modified gravity theory incorporating these effects, revealing new non-trivial solutions beyond General Relativity.

Contribution

It introduces a novel modified gravity theory by adding a topological torsion term derived from fermionic one-loop effects to the Einstein-Cartan action, highlighting new solutions.

Findings

The fermionic one-loop effective action includes topological invariants like Nieh-Yan and Chern-Simons terms.

The modified gravity theory reduces to GR under certain conditions.

A non-trivial solution exists where the modified equations differ from Einstein-Cartan theory.

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 topological nature since it can be linked with topological invariants from Riemann-Cartan spaces, like Nieh-Yan and Chern-Simons 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 non-trivial solution where the modified field equations do not reduce to the GR ones.