  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 renormalization group and construct the equations for the running of dimensionless parameters related to currents and for the effective Barbero-Immirzi parameter. 
Quantum Einstein-Cartan theory with the Holst term