Mixed gauge-gravity term and proper time

TL;DR

This work analyzes the one-loop effective action for Dirac spinors minimally coupled to a U(1) gauge field in a Maxwell–Einstein–Cartan (Riemann-Cartan) background. Using the Schwinger–DeWitt proper-time method, it derives finite gauge–torsion couplings, including a Carroll–Field–Jackiw (CFJ)–type term and the Nieh–Yan topological contribution, and discusses possible finite mixed curvature–torsion terms. The results suggest that torsion can act as a Lorentz-violating axial background, offering a mechanism for Lorentz symmetry breaking and providing a framework for LV terms in the SME when torsion is present. The study also indicates avenues for extending these results to non-Abelian gauge fields and to additional torsion–curvature–gauge couplings in future work.

Abstract

We consider the four-dimensional action of spinors minimally coupled to a $U(1)$-gauge field in an Riemann-Cartan background. In this theory, we integrate over the spinors and study the resulting one-loop gauge-gravity effective action, paying special attention to the contributions that depend on both the gauge field and the torsion. We explicitly calculate the gauge-torsion term, which turns out to be finite, and comment on possible terms depending simultaneously on torsion, curvature, and gauge field.