Field redefinitions and Plebanski formalism for GR

TL;DR

This paper explores a family of transformations acting on BF-type Lagrangians of gravity, revealing classically equivalent theories and deriving new formulations of General Relativity through field redefinitions in both chiral and non-chiral cases.

Contribution

It introduces a family of field redefinitions for BF-type gravity Lagrangians, leading to new formulations of GR, including a novel non-chiral BF plus potential formulation.

Findings

Derived an alternative chiral BF plus potential formulation of GR.

Established a new non-chiral BF plus potential formulation of GR.

Discussed the non-chiral pure connection formulation.

Abstract

We point out that there exists a family of transformations acting on BF-type Lagrangians of gravity, with Lagrangians related by such a transformation corresponding to classically equivalent theories. A transformation of this type corresponds to a particular field redefinition. We discuss both the chiral and non-chiral cases. In the chiral case there is a one-parameter, and in the non-chiral case a two-parameter family of such transformations. In the chiral setup, we use these transformations to give an alternative derivation of the chiral BF plus potential formulation of General Relativity that was proposed recently. In the non-chiral case, we show that there is a new BF plus potential type formulation of GR. We also make some remarks on the non-chiral pure connection formulation.