Supersymmetric Holst action with matter coupling and parity violation

TL;DR

This paper constructs a general Holst action framework for various supergravities, demonstrating that the Immirzi parameter does not affect field equations and highlighting parity violation due to Holst extension.

Contribution

It provides a unified construction of supersymmetric Holst actions for multiple supergravity theories, including matter couplings, and analyzes their invariance and parity properties.

Findings

Immirzi parameter does not influence field equations in these theories

Holst extension breaks parity symmetry

Constructs supersymmetric Holst actions for N=1, 2, 4, 8 supergravities

Abstract

A general construction of the Holst action is discussed. Based on this, the N = 1, 2, 4, 8 supergravities and N = 1 supergravities with matter coupling are presented. It is shown that in all this cases the Immirzi parameter dose not influence the field equations. The construction ensures that the theory is invariant under supersymmetry as well as gauge transformations, but the Holst extension breaks parity.