BF Description of Higher-Dimensional Gravity Theories

Abstract

It is well known that, in the first-order formalism, pure three-dimensional gravity is just the BF theory. Similarly, four-dimensional general relativity can be formulated as BF theory with an additional constraint term added to the Lagrangian. In this paper we show that the same is true also for higher-dimensional Einstein gravity: in any dimension gravity can be described as a constrained BF theory. Moreover, in any dimension these constraints are quadratic in the B field. After describing in details the structure of these constraints, we scketch the ``spin foam'' quantization of these theories, which proves to be quite similar to the spin foam quantization of general relativity in three and four dimensions. In particular, in any dimension, we solve the quantum constraints and find the so-called simple representations and intertwiners. These exhibit a simple and beautiful structure that is common to all dimensions.

26 pages, Revtex; minor changes

References in corpus (2)

• Spin Foam Models
• ``Sum over Surfaces'' form of Loop Quantum Gravity

Cited by in corpus (10)

• Cosmological Deformation of Lorentzian Spin Foam Models
• Newtonian gravity in loop quantum gravity
• Simple Spin Networks as Feynman Graphs
• Classical general relativity as BF-Plebanski theory with linear constraints
• Timelike surfaces in Lorentz covariant loop gravity and spin foam models
• Different types of torsion and their effect on the dynamics of fields
• Reality Conditions for Spin Foams
• Spin Foams for the Real, Complex Orthogonal Groups in 4D and the bivector scalar product reality constraint
• A Systematic Derivation of the Riemannian Barrett-Crane Intertwiner
• Spin Foams for the SO(4,C) BF theory and the SO(4,C) General Relativity