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

SIGMA 8 (2012), 052, 31 pages      arXiv:1204.5394      https://doi.org/10.3842/SIGMA.2012.052
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

Discrete Gravity Models and Loop Quantum Gravity: a Short Review

Maïté Dupuis a, James P. Ryan b and Simone Speziale c
a) Institute for Theoretical Physics III, University of Erlangen-Nürnberg, Erlangen, Germany
b) MPI für Gravitationsphysik, Am Mühlenberg 1, D-14476 Potsdam, Germany
c) Centre de Physique Théorique, CNRS-UMR 7332, Luminy Case 907, 13288 Marseille, France

Received April 25, 2012, in final form August 06, 2012; Published online August 13, 2012

Abstract
We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the spin foam formalism, with particular attention to the definition of the simplicity constraints.

Key words: Loop Quantum Gravity; discrete gravity; Regge calculus; simplicity constraints; twisted geometries.

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