Alternative derivation of Krasnov's action for general relativity

TL;DR

This paper derives Krasnov's action for general relativity from Plebanski's formulation by integrating out auxiliary fields and confirms its Hamiltonian structure aligns with Ashtekar's formalism.

Contribution

It provides a new derivation of Krasnov's action directly from Plebanski's formulation, clarifying its Hamiltonian structure.

Findings

Krasnov's action can be derived from Plebanski's action by integrating out auxiliary fields.

The Hamiltonian analysis shows constraints match those of Ashtekar's formalism.

The approach offers a clearer understanding of the relation between different formulations of general relativity.

Abstract

Starting from Plebanski's action for general relativity with cosmological constant, we show that by integrating out all the auxiliary fields Krasnov's action immediately emerges. We also perform the Hamiltonian analysis of the latter and show that the constraints are those of the Ashtekar formalism.