Physical effects of the Immirzi parameter in loop quantum gravity

The Immirzi parameter is a constant appearing in the general-relativity action used as a starting point for the loop quantization of gravity. The parameter is commonly believed not to appear in the equations of motion and not to have any physical effect besides nonperturbatrive quantum gravity. We show that this is not true in general: in the presence of minimally coupled fermions, the parameter appears in the equations of motion: it determines the coupling constant of a four-fermion interaction. Under some general assumptions, there is therefore a relation between the Immirzi parameter and physical effects that are observable in principle, independently from nonperturbative quantum gravity