On the Relations between Gravity and BF Theories

Abstract

We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both self-dual and non-chiral formulations, their generalizations, and the MacDowell-Mansouri action.

v3: journal typeset version

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Cited by in corpus (23)

• Twisted Gauge Theory Model of Topological Phases in Three Dimensions
• Pregeometric First Order Yang-Mills Theory
• The Construction of Spin Foam Vertex Amplitudes
• Exploring Cartan gravity with dynamical symmetry breaking
• $L_{\infty }$-Algebras of Einstein-Cartan-Palatini Gravity
• Topological Features of the Quantum Vacuum
• Entanglement entropy and correlations in loop quantum gravity
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• Spin connection formulations of real Lorentzian General Relativity
• Three-dimensional Background Field Gravity: A Hamilton-Jacobi analysis
• The Quantum Gravity Disk: Discrete Current Algebra
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• Gravity with torsion as deformed $BF$ theory
• Black hole and cosmological analysis of BF sequestered gravity
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• Covariant momentum map for non-Abelian topological BF field theory
• Field redefinitions and Plebanski formalism for GR
• Constraint Analysis of Two-Dimensional Quadratic Gravity from BF Theory
• Effective Lagrangian for Non-Abelian Two-Dimensional Topological Field Theory
• Combinatorial Cell Complexes: Duality, reconstruction and causal cobordisms
• Spin current in BF theory
• Non-Abelian gauge theories invariant under diffeomorphisms
• Hamilton-Jacobi analysis of the four dimensional BF model with cosmological term