$BF$ gravity

TL;DR

This paper reviews $BF$ gravity, a class of formulations of gravity based on deformations of $BF$ theory, highlighting their classical and quantum insights, especially in relation to spinfoam models.

Contribution

It provides a comprehensive, self-contained review of $BF$ formulations of $D$-dimensional general relativity, including new results and a unified treatment.

Findings

Deepened understanding of $BF$ formulations in classical gravity

Insights into quantum aspects and spinfoam models

Unified treatment of $D$-dimensional cases

Abstract

$BF$ gravity comprises all the formulations of gravity that are based on deformations of $BF$ theory. Such deformations consist of either constraints or potential terms added to the topological $BF$ action that turn some of the gauge degrees of freedom into physical ones, particularly giving rise to general relativity. The $BF$ formulations have provided new and deep insights into many classical and quantum aspects of the gravitational field, setting the foundations for the approach to quantum gravity known as spinfoam models. In this review, we present a self-contained and unified treatment of the $BF$ formulations of $D$-dimensional general relativity and other related models, focusing on the classical aspects of them and including some new results.