Torsion in Gauge Theory

Abstract

The potential conflict between torsion and gauge symmetry in the Riemann-Cartan curved space-time was noted by Kibble in his 1961 pioneering paper, and has since been discussed by many authors. Kibble suggested that, to preserve gauge symmetry, one should forgo the covariant derivative in favor of the ordinary derivative in the definition of the field strength F_μν for massless gauge theories, while for massive vector fields covariant derivatives should be adopted. This view was further emphasized by Hehl and collaborators in their influential 1976 review paper. We address the question of whether this deviation from normal procedure of forgoing covariant derivatives in curved spacetime with torsion could give rise to inconsistencies in the theory, such as the quantum renormalizability of a realistic interacting theory. We demonstrate in this note the one-loop renormalizability of a realistic gauge theory of gauge bosons interacting with Dirac spinors, such as the SU(3) chromodynamics, for the case of a curved Riemann-Cartan spacetime with totally anti-symmetric torsion. This affirmative confirmation is one step towards providing justification for the assertion that the flat-space definition of the gauge field strength should be adopted as the proper definition.