Quantum Einstein–Cartan theory with the Holst term

The Holst term represents an interesting addition to the Einstein–Cartan theory of gravity with torsion. When this term is present the contact interactions between vector and axial vector fermion currents gain an extra parity-violating component. We re-derive this interaction using a simple representation for the Holst term. The same representation serves as a useful basis for the calculation of one-loop divergences in the theory with external fermionic currents and cosmological constant. Furthermore, we explore the possibilities of the on-shell version of the renormalization group and construct equations for the running of dimensionless parameters related to currents and for the effective Barbero–Immirzi parameter. (paper)