Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 032, 15 pages      arXiv:1201.4247      https://doi.org/10.3842/SIGMA.2012.032
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

On the Relations between Gravity and BF Theories

Laurent Freidel a and Simone Speziale b
a) Perimeter Institute, 31 Caroline St N, Waterloo ON, N2L 2Y5, Canada
b) Centre de Physique Théorique, CNRS-UMR 7332, Luminy Case 907, 13288 Marseille, France

Received January 23, 2012, in final form May 18, 2012; Published online May 26, 2012

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.

Key words: Plebanski action; MacDowell-Mansouri action; BF gravity; TQFT; modified theories of gravity.

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