# $BF$ gravity

@inproceedings{Celada2016BFG, title={\$BF\$ gravity}, author={Mariano Celada and Diego L. Gonz'alez and Merced Montesinos}, year={2016} }

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…

## 34 Citations

Polynomial
BF
-type action for general relativity and anti-self-dual gravity

- PhysicsPhysical Review D
- 2018

We report a gravitational $BF$-type action principle propagating two (complex) degrees of freedom that, besides the gauge connection and the $B$ field, only employs an additional Lagrange multiplier.…

Poincaré–Plebański formulation of GR and dual simplicity constraints

- MathematicsClassical and Quantum Gravity
- 2018

We revise the classical continuum formulation behind the Spin Foam approach to the quantization of gravity. Based on the recent applications of the current EPRL-FK model beyond triangulations, we…

Canonical analysis of $BF$ gravity in $n$ dimensions

- Physics
- 2020

In this paper we perform in a manifestly $SO(n-1,1)$ [or, alternatively $SO(n)$] covariant fashion, the canonical analysis of general relativity in $n$ dimensions written as a constrained $BF$…

Construction and examples of higher gauge theories

- Mathematics
- 2020

We provide several examples of higher gauge theories, constructed as generalizations of a BF model to 2BF and 3BF models with constraints. Using the framework of higher category theory, we introduce…

Canonical analysis with no second-class constraints of
BF
gravity with Immirzi parameter

- PhysicsPhysical Review D
- 2020

In this paper we revisit the canonical analysis of $BF$ gravity with the Immirzi parameter and a cosmological constant. By examining the constraint on the $B$ field, we realize that the analysis can…

Higher gauge theories based on 3-groups

- PhysicsJournal of High Energy Physics
- 2019

A bstractWe study the categorical generalizations of a BF theory to 2BF and 3BF theories, corresponding to 2-groups and 3-groups, in the framework of higher gauge theory. In particular, we construct…

Covariant origin of the U(1)3 model for Euclidean quantum gravity

- MathematicsClassical and Quantum Gravity
- 2021

If one replaces the constraints of the Ashtekar–Barbero SU(2) gauge theory formulation of Euclidean gravity by their U(1)3 version, one arrives at a consistent model which captures significant…

On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity

- Mathematics
- 2019

Spin Foam and Loop approaches to Quantum Gravity reformulate Einstein's theory of relativity in terms of connection variables. The metric properties are encoded in face bivectors/conjugate fluxes…

Topological features of the quantum vacuum

- PhysicsPhysical Review D
- 2020

A central aspect of the cosmological constant problem is to understand why vacuum energy does not gravitate. In order to account for this observation, while allowing for nontrivial dynamics of the…

Different types of torsion and their effect on the dynamics of fields

- PhysicsThe European Physical Journal Plus
- 2018

Abstract.One of the formalisms that conveniently introduces torsion in gravity is the vierbein-Einstein-Palatini (VEP) formalism. The independent variables are the vierbein (tetrads) and the…

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