Holst actions for supergravity theories

Abstract

The Holst action containing the Immirzi parameter for pure gravity is generalized to supergravity theories. Supergravity equations of motion are not modified by such generalizations, thus preserving supersymmetry. Dependence on the Immirzi parameter does not emerge in the classical equations of motion. This is in contrast with the recent observation of Perez and Rovelli for gravity action containing the original Holst term and a minimally coupled Dirac fermion, where the classical equations of motion do develop a dependence on the Immirzi parameter.