Propagating torsion in 3D gravity and dynamical mass generation

Abstract

In this paper, fermions are minimally coupled to 3D gravity with dynamical torsion. A Kalb–Ramond field is also introduced and non-minimally coupled to the fermions in a gauge-invariant way. We show that a 1-loop mass generation mechanism takes place for both the 2-form gauge field and the torsion. As for the fermions, no mass is dynamically generated: at 1-loop, there is only a fermion mass shift proportional to the Yukawa coupling whenever these fermions have a non-vanishing tree-level mass.