Mixed gauge-gravity term and proper time

TL;DR

This paper computes the one-loop effective action for spinors in a Riemann-Cartan background, focusing on gauge-torsion interactions, revealing a finite gauge-torsion term and discussing combined torsion, curvature, and gauge field effects.

Contribution

It provides an explicit calculation of the finite gauge-torsion term in the one-loop effective action for spinors in Riemann-Cartan spacetime, highlighting mixed gauge-gravity-torsion interactions.

Findings

Finite gauge-torsion term explicitly calculated.

Discussion of potential terms involving torsion, curvature, and gauge fields.

Insights into quantum effects of torsion in gauge theories.

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.