Towards Perturbative Unimodular Poincaré Gauge Theories with Propagating Torsion

Abstract

We study the one-loop relation between an effective-field-theory extension of Poincaré gauge theories of gravity with propagating torsion and its unimodular counterpart. In the Einstein representation, we consider two representative quadratic torsion subsectors, namely totally antisymmetric (axial) torsion and the vector component of hook-antisymmetric torsion. On maximally symmetric metric backgrounds with vanishing background torsion, the diffeomorphism-invariant and genuine unimodular theories yield identical one-loop determinants in both sectors, reproducing the same local logarithmic divergences. We further examine flat backgrounds with homogeneous axial or vector torsion, where metric-torsion mixing is present. In each case, the torsion-dependent one-loop effective action in unimodular gauge and in the genuine unimodular formulation is controlled by the same physical determinant. Thus, for the actions and backgrounds considered, the unimodular constraint does not modify local one-loop torsion dynamics. We also delineate the limitations of this equivalence and the extensions needed for generic torsionful curved backgrounds.