Holst Actions for Supergravity Theories

TL;DR

This paper extends the Holst action with Immirzi parameter to supergravity theories, showing that classical equations remain unaffected and supersymmetry is preserved, unlike in gravity with fermions where Immirzi dependence appears.

Contribution

It generalizes the Holst action to supergravity, demonstrating that the Immirzi parameter does not influence classical equations or supersymmetry.

Findings

Supergravity equations of motion are unchanged by the generalized Holst action.

Supersymmetry is preserved in the generalized action.

Classical equations do not depend on the Immirzi parameter.

Abstract

Holst action containing Immirzi parameter for pure gravity is generalised to the supergravity theories. Supergravity equations of motion are not modified by such generalisations, 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 original Holst term and a minimally coupled Dirac fermion where the classical equations of motion do develop a dependence on Immirzi parameter.