On Dual Formulation of Gravity

TL;DR

This paper explores a novel dual formulation of gravity focusing on the Lorentz connection as the primary dynamical field, utilizing dualization in (Anti) de Sitter space, revealing connections with exotic interactions in three dimensions.

Contribution

It introduces a dual gravity formulation based on the Lorentz connection in (Anti) de Sitter space, differing from traditional tetrad or metric approaches.

Findings

Dual formulation relates to exotic parity-violating interactions in 3D

Uses first order parent Lagrangians in (Anti) de Sitter space

Potential new perspectives on gravity's fundamental structure

Abstract

In this paper we consider a possibility to construct dual formulation of gravity where the main dynamical field is the Lorentz connection \omega_\mu^{ab} and not that of tetrad e_\mu^a or metric g_\mu\nu. Our approach is based on the usual dualization procedure which uses first order parent Lagrangians but in (Anti) de Sitter space and not in the flat Minkowski one. It turns out that in d=3 dimensions such dual formulation is related with the so called exotic parity-violating interactions for massless spin-2 particles.