Barbero-Immirzi parameter in Regge calculus

Abstract

We consider Regge calculus in the representation in terms of area tensors and self- and antiselfdual connections generalised to the case of Holst action that is standard Einstein action in the tetrad-connection variables plus topological (on equations of motion for connections) term with coefficient $1/\gamma$, $\gamma$ is Barbero-Immirzi parameter. The quantum measure is shown to exponentially decrease with areas with typical cut-off scales $4\pi G$ and $4\pi G\gamma$ in spacelike and timelike regions, respectively ($G$ is the Newton constant).